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Editor’s Choice Articles

Editor’s Choice articles are based on recommendations by the scientific editors of MDPI journals from around the world. Editors select a small number of articles recently published in the journal that they believe will be particularly interesting to readers, or important in the respective research area. The aim is to provide a snapshot of some of the most exciting work published in the various research areas of the journal.

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12 pages, 690 KiB  
Article
Fundamental Relation for Gas of Interacting Particles in a Heat Flow
by Robert Hołyst, Karol Makuch, Konrad Giżyński, Anna Maciołek and Paweł J. Żuk
Entropy 2023, 25(9), 1295; https://doi.org/10.3390/e25091295 - 04 Sep 2023
Cited by 4 | Viewed by 1119
Abstract
There is a long-standing question of whether it is possible to extend the formalism of equilibrium thermodynamics to the case of nonequilibrium systems in steady-states. We have made such an extension for an ideal gas in a heat flow. Here, we investigated whether [...] Read more.
There is a long-standing question of whether it is possible to extend the formalism of equilibrium thermodynamics to the case of nonequilibrium systems in steady-states. We have made such an extension for an ideal gas in a heat flow. Here, we investigated whether such a description exists for the system with interactions: the van der Waals gas in a heat flow. We introduced a steady-state fundamental relation and the parameters of state, each associated with a single way of changing energy. The first law of nonequilibrium thermodynamics follows from these parameters. The internal energy U for the nonequilibrium states has the same form as in equilibrium thermodynamics. For the van der Waals gas, U(S*,V,N,a*,b*) is a function of only five parameters of state (irrespective of the number of parameters characterizing the boundary conditions): the effective entropy S*, volume V, number of particles N, and rescaled van der Waals parameters a*, b*. The state parameters, a*, b*, together with S*, determine the net heat exchange with the environment. The net heat differential does not have an integrating factor. As in equilibrium thermodynamics, the steady-state fundamental equation also leads to the thermodynamic Maxwell relations for measurable steady-state properties. Full article
(This article belongs to the Special Issue Entropy Production and Nonequilibrium Thermodynamics in Materials)
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17 pages, 464 KiB  
Opinion
Senses along Which the Entropy Sq Is Unique
by Constantino Tsallis
Entropy 2023, 25(5), 743; https://doi.org/10.3390/e25050743 - 01 May 2023
Cited by 6 | Viewed by 1524
Abstract
The Boltzmann–Gibbs–von Neumann–Shannon additive entropy SBG=−k∑ipilnpi as well as its continuous and quantum counterparts, constitute the grounding concept on which the BG statistical mechanics is constructed. This magnificent theory has produced, [...] Read more.
The Boltzmann–Gibbs–von Neumann–Shannon additive entropy SBG=−k∑ipilnpi as well as its continuous and quantum counterparts, constitute the grounding concept on which the BG statistical mechanics is constructed. This magnificent theory has produced, and will most probably keep producing in the future, successes in vast classes of classical and quantum systems. However, recent decades have seen a proliferation of natural, artificial and social complex systems which defy its bases and make it inapplicable. This paradigmatic theory has been generalized in 1988 into the nonextensive statistical mechanics—as currently referred to—grounded on the nonadditive entropy Sq=k1−∑ipiqq−1 as well as its corresponding continuous and quantum counterparts. In the literature, there exist nowadays over fifty mathematically well defined entropic functionals. Sq plays a special role among them. Indeed, it constitutes the pillar of a great variety of theoretical, experimental, observational and computational validations in the area of complexity—plectics, as Murray Gell-Mann used to call it. Then, a question emerges naturally, namely In what senses is entropy Sq unique? The present effort is dedicated to a—surely non exhaustive—mathematical answer to this basic question. Full article
(This article belongs to the Special Issue The Statistical Foundations of Entropy II)
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15 pages, 2994 KiB  
Review
Quantum Chaos and Level Dynamics
by Jakub Zakrzewski
Entropy 2023, 25(3), 491; https://doi.org/10.3390/e25030491 - 13 Mar 2023
Cited by 4 | Viewed by 1338
Abstract
We review the application of level dynamics to spectra of quantally chaotic systems. We show that the statistical mechanics approach gives us predictions about level statistics intermediate between integrable and chaotic dynamics. Then we discuss in detail different statistical measures involving level dynamics, [...] Read more.
We review the application of level dynamics to spectra of quantally chaotic systems. We show that the statistical mechanics approach gives us predictions about level statistics intermediate between integrable and chaotic dynamics. Then we discuss in detail different statistical measures involving level dynamics, such as level avoided-crossing distributions, level slope distributions, or level curvature distributions. We show both the aspects of universality in these distributions and their limitations. We concentrate in some detail on measures imported from the quantum information approach such as the fidelity susceptibility, and more generally, geometric tensor matrix elements. The possible open problems are suggested. Full article
(This article belongs to the Special Issue Quantum Chaos—Dedicated to Professor Giulio Casati on the Occasion of His 80th Birthday)
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15 pages, 418 KiB  
Article
Design and Analysis of Joint Group Shuffled Scheduling Decoding Algorithm for Double LDPC Codes System
by Qiwang Chen, Yanzhao Ren, Lin Zhou, Chen Chen and Sanya Liu
Entropy 2023, 25(2), 357; https://doi.org/10.3390/e25020357 - 15 Feb 2023
Cited by 3 | Viewed by 1210
Abstract
In this paper, a joint group shuffled scheduling decoding (JGSSD) algorithm for a joint source-channel coding (JSCC) scheme based on double low-density parity-check (D-LDPC) codes is presented. The proposed algorithm considers the D-LDPC coding structure as a whole and applies shuffled scheduling to [...] Read more.
In this paper, a joint group shuffled scheduling decoding (JGSSD) algorithm for a joint source-channel coding (JSCC) scheme based on double low-density parity-check (D-LDPC) codes is presented. The proposed algorithm considers the D-LDPC coding structure as a whole and applies shuffled scheduling to each group; the grouping relies on the types or the length of the variable nodes (VNs). By comparison, the conventional shuffled scheduling decoding algorithm can be regarded as a special case of this proposed algorithm. A novel joint extrinsic information transfer (JEXIT) algorithm for the D-LDPC codes system with the JGSSD algorithm is proposed, by which the source and channel decoding are calculated with different grouping strategies to analyze the effects of the grouping strategy. Simulation results and comparisons verify the superiority of the JGSSD algorithm, which can adaptively trade off the decoding performance, complexity and latency. Full article
(This article belongs to the Special Issue Coding and Entropy)
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12 pages, 574 KiB  
Article
Toward Prediction of Financial Crashes with a D-Wave Quantum Annealer
by Yongcheng Ding, Javier Gonzalez-Conde, Lucas Lamata, José D. Martín-Guerrero, Enrique Lizaso, Samuel Mugel, Xi Chen, Román Orús, Enrique Solano and Mikel Sanz
Entropy 2023, 25(2), 323; https://doi.org/10.3390/e25020323 - 10 Feb 2023
Cited by 22 | Viewed by 3040
Abstract
The prediction of financial crashes in a complex financial network is known to be an NP-hard problem, which means that no known algorithm can efficiently find optimal solutions. We experimentally explore a novel approach to this problem by using a D-Wave quantum annealer, [...] Read more.
The prediction of financial crashes in a complex financial network is known to be an NP-hard problem, which means that no known algorithm can efficiently find optimal solutions. We experimentally explore a novel approach to this problem by using a D-Wave quantum annealer, benchmarking its performance for attaining a financial equilibrium. To be specific, the equilibrium condition of a nonlinear financial model is embedded into a higher-order unconstrained binary optimization (HUBO) problem, which is then transformed into a spin-1/2 Hamiltonian with at most, two-qubit interactions. The problem is thus equivalent to finding the ground state of an interacting spin Hamiltonian, which can be approximated with a quantum annealer. The size of the simulation is mainly constrained by the necessity of a large number of physical qubits representing a logical qubit with the correct connectivity. Our experiment paves the way for the codification of this quantitative macroeconomics problem in quantum annealers. Full article
(This article belongs to the Special Issue Quantum Control and Quantum Computing)
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17 pages, 3668 KiB  
Article
Sample, Fuzzy and Distribution Entropies of Heart Rate Variability: What Do They Tell Us on Cardiovascular Complexity?
by Paolo Castiglioni, Giampiero Merati, Gianfranco Parati and Andrea Faini
Entropy 2023, 25(2), 281; https://doi.org/10.3390/e25020281 - 02 Feb 2023
Cited by 6 | Viewed by 2430
Abstract
Distribution Entropy (DistEn) has been introduced as an alternative to Sample Entropy (SampEn) to assess the heart rate variability (HRV) on much shorter series without the arbitrary definition of distance thresholds. However, DistEn, considered a measure of cardiovascular complexity, differs substantially from SampEn [...] Read more.
Distribution Entropy (DistEn) has been introduced as an alternative to Sample Entropy (SampEn) to assess the heart rate variability (HRV) on much shorter series without the arbitrary definition of distance thresholds. However, DistEn, considered a measure of cardiovascular complexity, differs substantially from SampEn or Fuzzy Entropy (FuzzyEn), both measures of HRV randomness. This work aims to compare DistEn, SampEn, and FuzzyEn analyzing postural changes (expected to modify the HRV randomness through a sympatho/vagal shift without affecting the cardiovascular complexity) and low-level spinal cord injuries (SCI, whose impaired integrative regulation may alter the system complexity without affecting the HRV spectrum). We recorded RR intervals in able-bodied (AB) and SCI participants in supine and sitting postures, evaluating DistEn, SampEn, and FuzzyEn over 512 beats. The significance of “case” (AB vs. SCI) and “posture” (supine vs. sitting) was assessed by longitudinal analysis. Multiscale DistEn (mDE), SampEn (mSE), and FuzzyEn (mFE) compared postures and cases at each scale between 2 and 20 beats. Unlike SampEn and FuzzyEn, DistEn is affected by the spinal lesion but not by the postural sympatho/vagal shift. The multiscale approach shows differences between AB and SCI sitting participants at the largest mFE scales and between postures in AB participants at the shortest mSE scales. Thus, our results support the hypothesis that DistEn measures cardiovascular complexity while SampEn/FuzzyEn measure HRV randomness, highlighting that together these methods integrate the information each of them provides. Full article
(This article belongs to the Special Issue Assessing Complexity in Physiological Systems through Biomedical Signals Analysis II)
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13 pages, 1425 KiB  
Article
Quantum Bounds on the Generalized Lyapunov Exponents
by Silvia Pappalardi and Jorge Kurchan
Entropy 2023, 25(2), 246; https://doi.org/10.3390/e25020246 - 30 Jan 2023
Cited by 7 | Viewed by 1651
Abstract
We discuss the generalized quantum Lyapunov exponents Lq, defined from the growth rate of the powers of the square commutator. They may be related to an appropriately defined thermodynamic limit of the spectrum of the commutator, which plays the role of [...] Read more.
We discuss the generalized quantum Lyapunov exponents Lq, defined from the growth rate of the powers of the square commutator. They may be related to an appropriately defined thermodynamic limit of the spectrum of the commutator, which plays the role of a large deviation function, obtained from the exponents Lq via a Legendre transform. We show that such exponents obey a generalized bound to chaos due to the fluctuation–dissipation theorem, as already discussed in the literature. The bounds for larger q are actually stronger, placing a limit on the large deviations of chaotic properties. Our findings at infinite temperature are exemplified by a numerical study of the kicked top, a paradigmatic model of quantum chaos. Full article
(This article belongs to the Special Issue Quantum Chaos—Dedicated to Professor Giulio Casati on the Occasion of His 80th Birthday)
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17 pages, 354 KiB  
Article
Invariant-Parameterized Exact Evolution Operator for SU(2) Systems with Time-Dependent Hamiltonian
by Hiromichi Nakazato, Alessandro Sergi, Agostino Migliore and Antonino Messina
Entropy 2023, 25(1), 96; https://doi.org/10.3390/e25010096 - 03 Jan 2023
Cited by 5 | Viewed by 1344
Abstract
We report the step-by-step construction of the exact, closed and explicit expression for the evolution operator U(t) of a localized and isolated qubit in an arbitrary time-dependent field, which for concreteness we assume to be a magnetic field. Our approach [...] Read more.
We report the step-by-step construction of the exact, closed and explicit expression for the evolution operator U(t) of a localized and isolated qubit in an arbitrary time-dependent field, which for concreteness we assume to be a magnetic field. Our approach is based on the existence of two independent dynamical invariants that enter the expression of SU(2) by means of two strictly related time-dependent, real or complex, parameters. The usefulness of our approach is demonstrated by exactly solving the quantum dynamics of a qubit subject to a controllable time-dependent field that can be realized in the laboratory. We further discuss possible applications to any SU(2) model, as well as the applicability of our method to realistic physical scenarios with different symmetry properties. Full article
(This article belongs to the Special Issue Quantum Nonstationary Systems)
18 pages, 1344 KiB  
Article
COVID-19 Effects on the Relationship between Cryptocurrencies: Can It Be Contagion? Insights from Econophysics Approaches
by Dora Almeida, Andreia Dionísio, Isabel Vieira and Paulo Ferreira
Entropy 2023, 25(1), 98; https://doi.org/10.3390/e25010098 - 03 Jan 2023
Cited by 4 | Viewed by 1610
Abstract
Cryptocurrencies are relatively new and innovative financial assets. They are a topic of interest to investors and academics due to their distinctive features. Whether financial or not, extraordinary events are one of the biggest challenges facing financial markets. The onset of the COVID-19 [...] Read more.
Cryptocurrencies are relatively new and innovative financial assets. They are a topic of interest to investors and academics due to their distinctive features. Whether financial or not, extraordinary events are one of the biggest challenges facing financial markets. The onset of the COVID-19 pandemic crisis, considered by some authors a “black swan”, is one of these events. In this study, we assess integration and contagion in the cryptocurrency market in the COVID-19 pandemic context, using two entropy-based measures: mutual information and transfer entropy. Both methodologies reveal that cryptocurrencies exhibit mixed levels of integration before and after the onset of the pandemic. Cryptocurrencies displaying higher integration before the event experienced a decline in such link after the world became aware of the first cases of pneumonia in Wuhan city. In what concerns contagion, mutual information provided evidence of its presence solely for the Huobi Token, and the transfer entropy analysis pointed out Tether and Huobi Token as its main source. As both analyses indicate no contagion from the pandemic turmoil to these financial assets, cryptocurrencies may be good investment options in case of real global shocks, such as the one provoked by the COVID-19 outbreak. Full article
(This article belongs to the Special Issue Cryptocurrency Behavior under Econophysics Approaches)
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31 pages, 1844 KiB  
Article
Extreme Eigenvalues and the Emerging Outlier in Rank-One Non-Hermitian Deformations of the Gaussian Unitary Ensemble
by Yan V. Fyodorov, Boris A. Khoruzhenko and Mihail Poplavskyi
Entropy 2023, 25(1), 74; https://doi.org/10.3390/e25010074 - 30 Dec 2022
Cited by 3 | Viewed by 1358
Abstract
Complex eigenvalues of random matrices J=GUE+iγdiag(1,0,…,0) provide the simplest model for studying resonances in wave scattering from a quantum chaotic system via a single open channel. It is [...] Read more.
Complex eigenvalues of random matrices J=GUE+iγdiag(1,0,…,0) provide the simplest model for studying resonances in wave scattering from a quantum chaotic system via a single open channel. It is known that in the limit of large matrix dimensions N≫1 the eigenvalue density of J undergoes an abrupt restructuring at γ=1, the critical threshold beyond which a single eigenvalue outlier (“broad resonance”) appears. We provide a detailed description of this restructuring transition, including the scaling with N of the width of the critical region about the outlier threshold γ=1 and the associated scaling for the real parts (“resonance positions”) and imaginary parts (“resonance widths”) of the eigenvalues which are farthest away from the real axis. In the critical regime we determine the density of such extreme eigenvalues, and show how the outlier gradually separates itself from the rest of the extreme eigenvalues. Finally, we describe the fluctuations in the height of the eigenvalue outlier for large but finite N in terms of the associated large deviation function. Full article
(This article belongs to the Special Issue Quantum Chaos—Dedicated to Professor Giulio Casati on the Occasion of His 80th Birthday)
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52 pages, 9913 KiB  
Review
Quantum Chaos in the Dynamics of Molecules
by Kazuo Takatsuka
Entropy 2023, 25(1), 63; https://doi.org/10.3390/e25010063 - 29 Dec 2022
Cited by 3 | Viewed by 2546
Abstract
Quantum chaos is reviewed from the viewpoint of “what is molecule?”, particularly placing emphasis on their dynamics. Molecules are composed of heavy nuclei and light electrons, and thereby the very basic molecular theory due to Born and Oppenheimer gives a view that quantum [...] Read more.
Quantum chaos is reviewed from the viewpoint of “what is molecule?”, particularly placing emphasis on their dynamics. Molecules are composed of heavy nuclei and light electrons, and thereby the very basic molecular theory due to Born and Oppenheimer gives a view that quantum electronic states provide potential functions working on nuclei, which in turn are often treated classically or semiclassically. Therefore, the classic study of chaos in molecular science began with those nuclear dynamics particularly about the vibrational energy randomization within a molecule. Statistical laws in probabilities and rates of chemical reactions even for small molecules of several atoms are among the chemical phenomena requiring the notion of chaos. Particularly the dynamics behind unimolecular decomposition are referred to as Intra-molecular Vibrational energy Redistribution (IVR). Semiclassical mechanics is also one of the main research fields of quantum chaos. We herein demonstrate chaos that appears only in semiclassical and full quantum dynamics. A fundamental phenomenon possibly giving birth to quantum chaos is “bifurcation and merging” of quantum wavepackets, rather than “stretching and folding” of the baker’s transformation and the horseshoe map as a geometrical foundation of classical chaos. Such wavepacket bifurcation and merging are indeed experimentally measurable as we showed before in the series of studies on real-time probing of nonadiabatic chemical reactions. After tracking these aspects of molecular chaos, we will explore quantum chaos found in nonadiabatic electron wavepacket dynamics, which emerges in the realm far beyond the Born-Oppenheimer paradigm. In this class of chaos, we propose a notion of Intra-molecular Nonadiabatic Electronic Energy Redistribution (INEER), which is a consequence of the chaotic fluxes of electrons and energy within a molecule. Full article
(This article belongs to the Special Issue Quantum Chaos—Dedicated to Professor Giulio Casati on the Occasion of His 80th Birthday)
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25 pages, 544 KiB  
Review
Diffusion Coefficient of a Brownian Particle in Equilibrium and Nonequilibrium: Einstein Model and Beyond
by Jakub Spiechowicz, Ivan G. Marchenko, Peter Hänggi and Jerzy Łuczka
Entropy 2023, 25(1), 42; https://doi.org/10.3390/e25010042 - 26 Dec 2022
Cited by 11 | Viewed by 4269
Abstract
The diffusion of small particles is omnipresent in many processes occurring in nature. As such, it is widely studied and exerted in almost all branches of sciences. It constitutes such a broad and often rather complex subject of exploration that we opt here [...] Read more.
The diffusion of small particles is omnipresent in many processes occurring in nature. As such, it is widely studied and exerted in almost all branches of sciences. It constitutes such a broad and often rather complex subject of exploration that we opt here to narrow our survey to the case of the diffusion coefficient for a Brownian particle that can be modeled in the framework of Langevin dynamics. Our main focus centers on the temperature dependence of the diffusion coefficient for several fundamental models of diverse physical systems. Starting out with diffusion in equilibrium for which the Einstein theory holds, we consider a number of physical situations outside of free Brownian motion and end by surveying nonequilibrium diffusion for a time-periodically driven Brownian particle dwelling randomly in a periodic potential. For this latter situation the diffusion coefficient exhibits an intriguingly non-monotonic dependence on temperature. Full article
(This article belongs to the Collection Foundations of Statistical Mechanics)
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12 pages, 296 KiB  
Article
Entanglement-Assisted Quantum Codes from Cyclic Codes
by Francisco Revson F. Pereira and Stefano Mancini
Entropy 2023, 25(1), 37; https://doi.org/10.3390/e25010037 - 24 Dec 2022
Cited by 9 | Viewed by 1393
Abstract
Entanglement-assisted quantum-error-correcting (EAQEC) codes are quantum codes which use entanglement as a resource. These codes can provide better error correction than the (entanglement unassisted) codes derived from the traditional stabilizer formalism. In this paper, we provide a general method to construct EAQEC codes [...] Read more.
Entanglement-assisted quantum-error-correcting (EAQEC) codes are quantum codes which use entanglement as a resource. These codes can provide better error correction than the (entanglement unassisted) codes derived from the traditional stabilizer formalism. In this paper, we provide a general method to construct EAQEC codes from cyclic codes. Afterwards, the method is applied to Reed–Solomon codes, BCH codes, and general cyclic codes. We use the Euclidean and Hermitian construction of EAQEC codes. Three families have been created: two families of EAQEC codes are maximal distance separable (MDS), and one is almost MDS or almost near MDS. The comparison of the codes in this paper is mostly based on the quantum Singleton bound. Full article
(This article belongs to the Special Issue Advances in Quantum Computing)
21 pages, 5934 KiB  
Article
Chaos and Thermalization in the Spin-Boson Dicke Model
by David Villaseñor, Saúl Pilatowsky-Cameo, Miguel A. Bastarrachea-Magnani, Sergio Lerma-Hernández, Lea F. Santos and Jorge G. Hirsch
Entropy 2023, 25(1), 8; https://doi.org/10.3390/e25010008 - 21 Dec 2022
Cited by 10 | Viewed by 1743
Abstract
We present a detailed analysis of the connection between chaos and the onset of thermalization in the spin-boson Dicke model. This system has a well-defined classical limit with two degrees of freedom, and it presents both regular and chaotic regions. Our studies of [...] Read more.
We present a detailed analysis of the connection between chaos and the onset of thermalization in the spin-boson Dicke model. This system has a well-defined classical limit with two degrees of freedom, and it presents both regular and chaotic regions. Our studies of the eigenstate expectation values and the distributions of the off-diagonal elements of the number of photons and the number of excited atoms validate the diagonal and off-diagonal eigenstate thermalization hypothesis (ETH) in the chaotic region, thus ensuring thermalization. The validity of the ETH reflects the chaotic structure of the eigenstates, which we corroborate using the von Neumann entanglement entropy and the Shannon entropy. Our results for the Shannon entropy also make evident the advantages of the so-called “efficient basis” over the widespread employed Fock basis when investigating the unbounded spectrum of the Dicke model. The efficient basis gives us access to a larger number of converged states than what can be reached with the Fock basis. Full article
(This article belongs to the Special Issue Quantum Chaos—Dedicated to Professor Giulio Casati on the Occasion of His 80th Birthday)
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25 pages, 2133 KiB  
Article
Canonical Density Matrices from Eigenstates of Mixed Systems
by Mahdi Kourehpaz, Stefan Donsa, Fabian Lackner, Joachim Burgdörfer and Iva Březinová
Entropy 2022, 24(12), 1740; https://doi.org/10.3390/e24121740 - 29 Nov 2022
Cited by 3 | Viewed by 5720
Abstract
One key issue of the foundation of statistical mechanics is the emergence of equilibrium ensembles in isolated and closed quantum systems. Recently, it was predicted that in the thermodynamic (N→∞) limit of large quantum many-body systems, canonical density matrices [...] Read more.
One key issue of the foundation of statistical mechanics is the emergence of equilibrium ensembles in isolated and closed quantum systems. Recently, it was predicted that in the thermodynamic (N→∞) limit of large quantum many-body systems, canonical density matrices emerge for small subsystems from almost all pure states. This notion of canonical typicality is assumed to originate from the entanglement between subsystem and environment and the resulting intrinsic quantum complexity of the many-body state. For individual eigenstates, it has been shown that local observables show thermal properties provided the eigenstate thermalization hypothesis holds, which requires the system to be quantum-chaotic. In the present paper, we study the emergence of thermal states in the regime of a quantum analog of a mixed phase space. Specifically, we study the emergence of the canonical density matrix of an impurity upon reduction from isolated energy eigenstates of a large but finite quantum system the impurity is embedded in. Our system can be tuned by means of a single parameter from quantum integrability to quantum chaos and corresponds in between to a system with mixed quantum phase space. We show that the probability for finding a canonical density matrix when reducing the ensemble of energy eigenstates of the finite many-body system can be quantitatively controlled and tuned by the degree of quantum chaos present. For the transition from quantum integrability to quantum chaos, we find a continuous and universal (i.e., size-independent) relation between the fraction of canonical eigenstates and the degree of chaoticity as measured by the Brody parameter or the Shannon entropy. Full article
(This article belongs to the Special Issue Quantum Chaos—Dedicated to Professor Giulio Casati on the Occasion of His 80th Birthday)
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13 pages, 356 KiB  
Article
Entropy Optimization, Generalized Logarithms, and Duality Relations
by Angel R. Plastino, Constantino Tsallis, Roseli S. Wedemann and Hans J. Haubold
Entropy 2022, 24(12), 1723; https://doi.org/10.3390/e24121723 - 25 Nov 2022
Cited by 5 | Viewed by 1471
Abstract
Several generalizations or extensions of the Boltzmann–Gibbs thermostatistics, based on non-standard entropies, have been the focus of considerable research activity in recent years. Among these, the power-law, non-additive entropies [...] Read more.
Several generalizations or extensions of the Boltzmann–Gibbs thermostatistics, based on non-standard entropies, have been the focus of considerable research activity in recent years. Among these, the power-law, non-additive entropies Sq≡k1−∑ipiqq−1(q∈R;S1=SBG≡−k∑ipilnpi) have harvested the largest number of successful applications. The specific structural features of the Sq thermostatistics, therefore, are worthy of close scrutiny. In the present work, we analyze one of these features, according to which the q-logarithm function lnqx≡x1−q−11−q(ln1x=lnx) associated with the Sq entropy is linked, via a duality relation, to the q-exponential function characterizing the maximum-entropy probability distributions. We enquire into which entropic functionals lead to this or similar structures, and investigate the corresponding duality relations. Full article
(This article belongs to the Special Issue Non-additive Entropy Formulas: Motivation and Derivations)
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23 pages, 5468 KiB  
Article
Functional Connectome of the Human Brain with Total Correlation
by Qiang Li, Greg Ver Steeg, Shujian Yu and Jesus Malo
Entropy 2022, 24(12), 1725; https://doi.org/10.3390/e24121725 - 25 Nov 2022
Cited by 5 | Viewed by 3098
Abstract
Recent studies proposed the use of Total Correlation to describe functional connectivity among brain regions as a multivariate alternative to conventional pairwise measures such as correlation or mutual information. In this work, we build on this idea to infer a large-scale (whole-brain) connectivity [...] Read more.
Recent studies proposed the use of Total Correlation to describe functional connectivity among brain regions as a multivariate alternative to conventional pairwise measures such as correlation or mutual information. In this work, we build on this idea to infer a large-scale (whole-brain) connectivity network based on Total Correlation and show the possibility of using this kind of network as biomarkers of brain alterations. In particular, this work uses Correlation Explanation (CorEx) to estimate Total Correlation. First, we prove that CorEx estimates of Total Correlation and clustering results are trustable compared to ground truth values. Second, the inferred large-scale connectivity network extracted from the more extensive open fMRI datasets is consistent with existing neuroscience studies, but, interestingly, can estimate additional relations beyond pairwise regions. And finally, we show how the connectivity graphs based on Total Correlation can also be an effective tool to aid in the discovery of brain diseases. Full article
(This article belongs to the Special Issue Applications of Information Theory in Neuroscience)
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11 pages, 3187 KiB  
Article
Quantum Coherence in Loopless Superconductive Networks
by Massimiliano Lucci, Valerio Campanari, Davide Cassi, Vittorio Merlo, Francesco Romeo, Gaetano Salina and Matteo Cirillo
Entropy 2022, 24(11), 1690; https://doi.org/10.3390/e24111690 - 18 Nov 2022
Cited by 2 | Viewed by 1146
Abstract
Measurements indicating that planar networks of superconductive islands connected by Josephson junctions display long-range quantum coherence are reported. The networks consist of superconducting islands connected by Josephson junctions and have a tree-like topological structure containing no loops. Enhancements of superconductive gaps over specific [...] Read more.
Measurements indicating that planar networks of superconductive islands connected by Josephson junctions display long-range quantum coherence are reported. The networks consist of superconducting islands connected by Josephson junctions and have a tree-like topological structure containing no loops. Enhancements of superconductive gaps over specific branches of the networks and sharp increases in pair currents are the main signatures of the coherent states. In order to unambiguously attribute the observed effects to branches being embedded in the networks, comparisons with geometrically equivalent—but isolated—counterparts are reported. Tuning the Josephson coupling energy by an external magnetic field generates increases in the Josephson currents, along the above-mentioned specific branches, which follow a functional dependence typical of phase transitions. Results are presented for double comb and star geometry networks, and in both cases, the observed effects provide positive quantitative evidence of the predictions of existing theoretical models. Full article
(This article belongs to the Special Issue Quantum Information and Quantum Optics)
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17 pages, 3674 KiB  
Article
Universal Single-Mode Lasing in Fully Chaotic Billiard Lasers
by Mengyu You, Daisuke Sakakibara, Kota Makino, Yonosuke Morishita, Kazutoshi Matsumura, Yuta Kawashima, Manao Yoshikawa, Mahiro Tonosaki, Kazutaka Kanno, Atsushi Uchida, Satoshi Sunada, Susumu Shinohara and Takahisa Harayama
Entropy 2022, 24(11), 1648; https://doi.org/10.3390/e24111648 - 14 Nov 2022
Cited by 4 | Viewed by 1692
Abstract
By numerical simulations and experiments of fully chaotic billiard lasers, we show that single-mode lasing states are stable, whereas multi-mode lasing states are unstable when the size of the billiard is much larger than the wavelength and the external pumping power is sufficiently [...] Read more.
By numerical simulations and experiments of fully chaotic billiard lasers, we show that single-mode lasing states are stable, whereas multi-mode lasing states are unstable when the size of the billiard is much larger than the wavelength and the external pumping power is sufficiently large. On the other hand, for integrable billiard lasers, it is shown that multi-mode lasing states are stable, whereas single-mode lasing states are unstable. These phenomena arise from the combination of two different nonlinear effects of mode-interaction due to the active lasing medium and deformation of the billiard shape. Investigations of billiard lasers with various shapes revealed that single-mode lasing is a universal phenomenon for fully chaotic billiard lasers. Full article
(This article belongs to the Special Issue Quantum Chaos—Dedicated to Professor Giulio Casati on the Occasion of His 80th Birthday)
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18 pages, 733 KiB  
Article
Dependency Structures in Cryptocurrency Market from High to Low Frequency
by Antonio Briola and Tomaso Aste
Entropy 2022, 24(11), 1548; https://doi.org/10.3390/e24111548 - 28 Oct 2022
Cited by 4 | Viewed by 1861
Abstract
We investigate logarithmic price returns cross-correlations at different time horizons for a set of 25 liquid cryptocurrencies traded on the FTX digital currency exchange. We study how the structure of the Minimum Spanning Tree (MST) and the Triangulated Maximally Filtered Graph (TMFG) evolve [...] Read more.
We investigate logarithmic price returns cross-correlations at different time horizons for a set of 25 liquid cryptocurrencies traded on the FTX digital currency exchange. We study how the structure of the Minimum Spanning Tree (MST) and the Triangulated Maximally Filtered Graph (TMFG) evolve from high (15 s) to low (1 day) frequency time resolutions. For each horizon, we test the stability, statistical significance and economic meaningfulness of the networks. Results give a deep insight into the evolutionary process of the time dependent hierarchical organization of the system under analysis. A decrease in correlation between pairs of cryptocurrencies is observed for finer time sampling resolutions. A growing structure emerges for coarser ones, highlighting multiple changes in the hierarchical reference role played by mainstream cryptocurrencies. This effect is studied both in its pairwise realizations and intra-sector ones. Full article
(This article belongs to the Special Issue Recent Trends and Developments in Econophysics)
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18 pages, 381 KiB  
Article
An Overview on Irreversible Port-Hamiltonian Systems
by Hector Ramirez and Yann Le Gorrec
Entropy 2022, 24(10), 1478; https://doi.org/10.3390/e24101478 - 17 Oct 2022
Cited by 4 | Viewed by 1651
Abstract
A comprehensive overview of the irreversible port-Hamiltonian system’s formulation for finite and infinite dimensional systems defined on 1D spatial domains is provided in a unified manner. The irreversible port-Hamiltonian system formulation shows the extension of classical port-Hamiltonian system formulations to cope with irreversible [...] Read more.
A comprehensive overview of the irreversible port-Hamiltonian system’s formulation for finite and infinite dimensional systems defined on 1D spatial domains is provided in a unified manner. The irreversible port-Hamiltonian system formulation shows the extension of classical port-Hamiltonian system formulations to cope with irreversible thermodynamic systems for finite and infinite dimensional systems. This is achieved by including, in an explicit manner, the coupling between irreversible mechanical and thermal phenomena with the thermal domain as an energy-preserving and entropy-increasing operator. Similarly to Hamiltonian systems, this operator is skew-symmetric, guaranteeing energy conservation. To distinguish from Hamiltonian systems, the operator depends on co-state variables and is, hence, a nonlinear-function in the gradient of the total energy. This is what allows encoding the second law as a structural property of irreversible port-Hamiltonian systems. The formalism encompasses coupled thermo-mechanical systems and purely reversible or conservative systems as a particular case. This appears clearly when splitting the state space such that the entropy coordinate is separated from other state variables. Several examples have been used to illustrate the formalism, both for finite and infinite dimensional systems, and a discussion on ongoing and future studies is provided. Full article
(This article belongs to the Special Issue Geometric Structure of Thermodynamics: Theory and Applications)
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29 pages, 670 KiB  
Article
“Yet Once More”: The Double-Slit Experiment and Quantum Discontinuity
by Arkady Plotnitsky
Entropy 2022, 24(10), 1455; https://doi.org/10.3390/e24101455 - 12 Oct 2022
Cited by 4 | Viewed by 1557
Abstract
This article reconsiders the double-slit experiment from the nonrealist or, in terms of this article, “reality-without-realism” (RWR) perspective, grounded in the combination of three forms of quantum discontinuity: (1) “Heisenberg discontinuity”, defined by the impossibility of a representation or even conception of how [...] Read more.
This article reconsiders the double-slit experiment from the nonrealist or, in terms of this article, “reality-without-realism” (RWR) perspective, grounded in the combination of three forms of quantum discontinuity: (1) “Heisenberg discontinuity”, defined by the impossibility of a representation or even conception of how quantum phenomena come about, even though quantum theory (such as quantum mechanics or quantum field theory) predicts the data in question strictly in accord with what is observed in quantum experiments); (2) “Bohr discontinuity”, defined, under the assumption of Heisenberg discontinuity, by the view that quantum phenomena and the data observed therein are described by classical and not quantum theory, even though classical physics cannot predict them; and (3) “Dirac discontinuity” (not considered by Dirac himself, but suggested by his equation), according to which the concept of a quantum object, such as a photon or electron, is an idealization only applicable at the time of observation and not to something that exists independently in nature. Dirac discontinuity is of particular importance for the article’s foundational argument and its analysis of the double-slit experiment. Full article
(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering)
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35 pages, 988 KiB  
Article
Revisiting Chernoff Information with Likelihood Ratio Exponential Families
by Frank Nielsen
Entropy 2022, 24(10), 1400; https://doi.org/10.3390/e24101400 - 01 Oct 2022
Cited by 6 | Viewed by 3825
Abstract
The Chernoff information between two probability measures is a statistical divergence measuring their deviation defined as their maximally skewed Bhattacharyya distance. Although the Chernoff information was originally introduced for bounding the Bayes error in statistical hypothesis testing, the divergence found many other applications [...] Read more.
The Chernoff information between two probability measures is a statistical divergence measuring their deviation defined as their maximally skewed Bhattacharyya distance. Although the Chernoff information was originally introduced for bounding the Bayes error in statistical hypothesis testing, the divergence found many other applications due to its empirical robustness property found in applications ranging from information fusion to quantum information. From the viewpoint of information theory, the Chernoff information can also be interpreted as a minmax symmetrization of the Kullback–Leibler divergence. In this paper, we first revisit the Chernoff information between two densities of a measurable Lebesgue space by considering the exponential families induced by their geometric mixtures: The so-called likelihood ratio exponential families. Second, we show how to (i) solve exactly the Chernoff information between any two univariate Gaussian distributions or get a closed-form formula using symbolic computing, (ii) report a closed-form formula of the Chernoff information of centered Gaussians with scaled covariance matrices and (iii) use a fast numerical scheme to approximate the Chernoff information between any two multivariate Gaussian distributions. Full article
(This article belongs to the Special Issue Robust Distance Metric Learning in the Framework of Statistical Information Theory)
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17 pages, 399 KiB  
Article
Information Theory for Biological Sequence Classification: A Novel Feature Extraction Technique Based on Tsallis Entropy
by Robson P. Bonidia, Anderson P. Avila Santos, Breno L. S. de Almeida, Peter F. Stadler, Ulisses Nunes da Rocha, Danilo S. Sanches and André C. P. L. F. de Carvalho
Entropy 2022, 24(10), 1398; https://doi.org/10.3390/e24101398 - 01 Oct 2022
Cited by 2 | Viewed by 1914
Abstract
In recent years, there has been an exponential growth in sequencing projects due to accelerated technological advances, leading to a significant increase in the amount of data and resulting in new challenges for biological sequence analysis. Consequently, the use of techniques capable of [...] Read more.
In recent years, there has been an exponential growth in sequencing projects due to accelerated technological advances, leading to a significant increase in the amount of data and resulting in new challenges for biological sequence analysis. Consequently, the use of techniques capable of analyzing large amounts of data has been explored, such as machine learning (ML) algorithms. ML algorithms are being used to analyze and classify biological sequences, despite the intrinsic difficulty in extracting and finding representative biological sequence methods suitable for them. Thereby, extracting numerical features to represent sequences makes it statistically feasible to use universal concepts from Information Theory, such as Tsallis and Shannon entropy. In this study, we propose a novel Tsallis entropy-based feature extractor to provide useful information to classify biological sequences. To assess its relevance, we prepared five case studies: (1) an analysis of the entropic index q; (2) performance testing of the best entropic indices on new datasets; (3) a comparison made with Shannon entropy and (4) generalized entropies; (5) an investigation of the Tsallis entropy in the context of dimensionality reduction. As a result, our proposal proved to be effective, being superior to Shannon entropy and robust in terms of generalization, and also potentially representative for collecting information in fewer dimensions compared with methods such as Singular Value Decomposition and Uniform Manifold Approximation and Projection. Full article
(This article belongs to the Special Issue Information Theory in Computational Biology)
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22 pages, 560 KiB  
Article
On Quantum Entropy
by Davi Geiger and Zvi M. Kedem
Entropy 2022, 24(10), 1341; https://doi.org/10.3390/e24101341 - 23 Sep 2022
Cited by 3 | Viewed by 4273
Abstract
Quantum physics, despite its intrinsically probabilistic nature, lacks a definition of entropy fully accounting for the randomness of a quantum state. For example, von Neumann entropy quantifies only the incomplete specification of a quantum state and does not quantify the probabilistic distribution of [...] Read more.
Quantum physics, despite its intrinsically probabilistic nature, lacks a definition of entropy fully accounting for the randomness of a quantum state. For example, von Neumann entropy quantifies only the incomplete specification of a quantum state and does not quantify the probabilistic distribution of its observables; it trivially vanishes for pure quantum states. We propose a quantum entropy that quantifies the randomness of a pure quantum state via a conjugate pair of observables/operators forming the quantum phase space. The entropy is dimensionless, it is a relativistic scalar, it is invariant under canonical transformations and under CPT transformations, and its minimum has been established by the entropic uncertainty principle. We expand the entropy to also include mixed states. We show that the entropy is monotonically increasing during a time evolution of coherent states under a Dirac Hamiltonian. However, in a mathematical scenario, when two fermions come closer to each other, each evolving as a coherent state, the total system’s entropy oscillates due to the increasing spatial entanglement. We hypothesize an entropy law governing physical systems whereby the entropy of a closed system never decreases, implying a time arrow for particle physics. We then explore the possibility that as the oscillations of the entropy must by the law be barred in quantum physics, potential entropy oscillations trigger annihilation and creation of particles. Full article
(This article belongs to the Special Issue Nature of Entropy and Its Direct Metrology)
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30 pages, 633 KiB  
Article
Assessing, Testing and Estimating the Amount of Fine-Tuning by Means of Active Information
by Daniel Andrés Díaz-Pachón and Ola Hössjer
Entropy 2022, 24(10), 1323; https://doi.org/10.3390/e24101323 - 21 Sep 2022
Cited by 6 | Viewed by 1506
Abstract
A general framework is introduced to estimate how much external information has been infused into a search algorithm, the so-called active information. This is rephrased as a test of fine-tuning, where tuning corresponds to the amount of pre-specified knowledge that the algorithm makes [...] Read more.
A general framework is introduced to estimate how much external information has been infused into a search algorithm, the so-called active information. This is rephrased as a test of fine-tuning, where tuning corresponds to the amount of pre-specified knowledge that the algorithm makes use of in order to reach a certain target. A function f quantifies specificity for each possible outcome x of a search, so that the target of the algorithm is a set of highly specified states, whereas fine-tuning occurs if it is much more likely for the algorithm to reach the target as intended than by chance. The distribution of a random outcome X of the algorithm involves a parameter θ that quantifies how much background information has been infused. A simple choice of this parameter is to use θf in order to exponentially tilt the distribution of the outcome of the search algorithm under the null distribution of no tuning, so that an exponential family of distributions is obtained. Such algorithms are obtained by iterating a Metropolis–Hastings type of Markov chain, which makes it possible to compute their active information under the equilibrium and non-equilibrium of the Markov chain, with or without stopping when the targeted set of fine-tuned states has been reached. Other choices of tuning parameters θ are discussed as well. Nonparametric and parametric estimators of active information and tests of fine-tuning are developed when repeated and independent outcomes of the algorithm are available. The theory is illustrated with examples from cosmology, student learning, reinforcement learning, a Moran type model of population genetics, and evolutionary programming. Full article
(This article belongs to the Special Issue Recent Advances in Statistical Theory and Applications)
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10 pages, 2358 KiB  
Article
Statistical Mechanics of Political Polarization
by Miron Kaufman, Sanda Kaufman and Hung T. Diep
Entropy 2022, 24(9), 1262; https://doi.org/10.3390/e24091262 - 08 Sep 2022
Cited by 8 | Viewed by 2493
Abstract
Rapidly increasing political polarization threatens democracies around the world. Scholars from several disciplines are assessing and modeling polarization antecedents, processes, and consequences. Social systems are complex and networked. Their constant shifting hinders attempts to trace causes of observed trends, predict their consequences, or [...] Read more.
Rapidly increasing political polarization threatens democracies around the world. Scholars from several disciplines are assessing and modeling polarization antecedents, processes, and consequences. Social systems are complex and networked. Their constant shifting hinders attempts to trace causes of observed trends, predict their consequences, or mitigate them. We propose an equivalent-neighbor model of polarization dynamics. Using statistical physics techniques, we generate anticipatory scenarios and examine whether leadership and/or external events alleviate or exacerbate polarization. We consider three highly polarized USA groups: Democrats, Republicans, and Independents. We assume that in each group, each individual has a political stance s ranging between left and right. We quantify the noise in this system as a “social temperature” T. Using energy E, we describe individuals’ interactions in time within their own group and with individuals of the other groups. It depends on the stance s as well as on three intra-group and six inter-group coupling parameters. We compute the probability distributions of stances at any time using the Boltzmann probability weight exp(−E/T). We generate average group-stance scenarios in time and explore whether concerted interventions or unexpected shocks can alter them. The results inform on the perils of continuing the current polarization trends, as well as on possibilities of changing course. Full article
(This article belongs to the Special Issue Statistical Physics of Opinion Formation and Social Phenomena)
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17 pages, 4479 KiB  
Article
Elastic Entropic Forces in Polymer Deformation
by Vladimir I. Kartsovnik and Dimitri Volchenkov
Entropy 2022, 24(9), 1260; https://doi.org/10.3390/e24091260 - 07 Sep 2022
Cited by 5 | Viewed by 1800
Abstract
The entropic nature of elasticity of long molecular chains and reticulated materials is discussed concerning the analysis of flows of polymer melts and elastomer deformation in the framework of Frenkel–Eyring molecular kinetic theory. Deformation curves are calculated in line with the simple viscoelasticity [...] Read more.
The entropic nature of elasticity of long molecular chains and reticulated materials is discussed concerning the analysis of flows of polymer melts and elastomer deformation in the framework of Frenkel–Eyring molecular kinetic theory. Deformation curves are calculated in line with the simple viscoelasticity models where the activation energy of viscous flow depends on the magnitude of elastic entropic forces of the stretched macromolecules. The interconnections between deformation processes and the structure of elastomer networks, as well as their mutual influence on each other, are considered. Full article
(This article belongs to the Special Issue Entropic Forces in Complex Systems II)
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11 pages, 1415 KiB  
Article
Decoding ‘Maximum Entropy’ Deconvolution
by Long V. Le, Tae Jung Kim, Young Dong Kim and David E. Aspnes
Entropy 2022, 24(9), 1238; https://doi.org/10.3390/e24091238 - 02 Sep 2022
Cited by 2 | Viewed by 3217
Abstract
For over five decades, the mathematical procedure termed “maximum entropy” (M-E) has been used to deconvolve structure in spectra, optical and otherwise, although quantitative measures of performance remain unknown. Here, we examine this procedure analytically for the lowest two orders for a Lorentzian [...] Read more.
For over five decades, the mathematical procedure termed “maximum entropy” (M-E) has been used to deconvolve structure in spectra, optical and otherwise, although quantitative measures of performance remain unknown. Here, we examine this procedure analytically for the lowest two orders for a Lorentzian feature, obtaining expressions for the amount of sharpening and identifying how spurious structures appear. Illustrative examples are provided. These results enhance the utility of this widely used deconvolution approach to spectral analysis. Full article
(This article belongs to the Special Issue Concepts of Entropy and Their Applications III)
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15 pages, 1850 KiB  
Article
A Bayesian Analysis of Plant DNA Length Distribution via κ-Statistics
by Maxsuel M. F. de Lima, Dory H. A. L. Anselmo, Raimundo Silva, Glauber H. S. Nunes, Umberto L. Fulco, Manoel S. Vasconcelos and Vamberto D. Mello
Entropy 2022, 24(9), 1225; https://doi.org/10.3390/e24091225 - 01 Sep 2022
Cited by 3 | Viewed by 1365
Abstract
We report an analysis of the distribution of lengths of plant DNA (exons). Three species of Cucurbitaceae were investigated. In our study, we used two distinct κ distribution functions, namely, κ-Maxwellian and double-κ, to fit the length distributions. To determine [...] Read more.
We report an analysis of the distribution of lengths of plant DNA (exons). Three species of Cucurbitaceae were investigated. In our study, we used two distinct κ distribution functions, namely, κ-Maxwellian and double-κ, to fit the length distributions. To determine which distribution has the best fitting, we made a Bayesian analysis of the models. Furthermore, we filtered the data, removing outliers, through a box plot analysis. Our findings show that the sum of κ-exponentials is the most appropriate to adjust the distribution curves and that the values of the κ parameter do not undergo considerable changes after filtering. Furthermore, for the analyzed species, there is a tendency for the κ parameter to lay within the interval (0.27;0.43). Full article
(This article belongs to the Special Issue Twenty Years of Kaniadakis Entropy: Current Trends and Future Perspectives)
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22 pages, 446 KiB  
Article
Efficiency of the Moscow Stock Exchange before 2022
by Andrey Shternshis, Piero Mazzarisi and Stefano Marmi
Entropy 2022, 24(9), 1184; https://doi.org/10.3390/e24091184 - 25 Aug 2022
Cited by 4 | Viewed by 1925
Abstract
This paper investigates the degree of efficiency for the Moscow Stock Exchange. A market is called efficient if prices of its assets fully reflect all available information. We show that the degree of market efficiency is significantly low for most of the months [...] Read more.
This paper investigates the degree of efficiency for the Moscow Stock Exchange. A market is called efficient if prices of its assets fully reflect all available information. We show that the degree of market efficiency is significantly low for most of the months from 2012 to 2021. We calculate the degree of market efficiency by (i) filtering out regularities in financial data and (ii) computing the Shannon entropy of the filtered return time series. We developed a simple method for estimating volatility and price staleness in empirical data in order to filter out such regularity patterns from return time series. The resulting financial time series of stock returns are then clustered into different groups according to some entropy measures. In particular, we use the Kullback–Leibler distance and a novel entropy metric capturing the co-movements between pairs of stocks. By using Monte Carlo simulations, we are then able to identify the time periods of market inefficiency for a group of 18 stocks. The inefficiency of the Moscow Stock Exchange that we have detected is a signal of the possibility of devising profitable strategies, net of transaction costs. The deviation from the efficient behavior for a stock strongly depends on the industrial sector that it belongs to. Full article
(This article belongs to the Special Issue Applications of Statistical Physics in Finance and Economics)
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19 pages, 5449 KiB  
Article
Monte Carlo Simulation of Stochastic Differential Equation to Study Information Geometry
by Abhiram Anand Thiruthummal and Eun-jin Kim
Entropy 2022, 24(8), 1113; https://doi.org/10.3390/e24081113 - 12 Aug 2022
Cited by 7 | Viewed by 1748
Abstract
Information Geometry is a useful tool to study and compare the solutions of a Stochastic Differential Equations (SDEs) for non-equilibrium systems. As an alternative method to solving the Fokker–Planck equation, we propose a new method to calculate time-dependent probability density functions (PDFs) and [...] Read more.
Information Geometry is a useful tool to study and compare the solutions of a Stochastic Differential Equations (SDEs) for non-equilibrium systems. As an alternative method to solving the Fokker–Planck equation, we propose a new method to calculate time-dependent probability density functions (PDFs) and to study Information Geometry using Monte Carlo (MC) simulation of SDEs. Specifically, we develop a new MC SDE method to overcome the challenges in calculating a time-dependent PDF and information geometric diagnostics and to speed up simulations by utilizing GPU computing. Using MC SDE simulations, we reproduce Information Geometric scaling relations found from the Fokker–Planck method for the case of a stochastic process with linear and cubic damping terms. We showcase the advantage of MC SDE simulation over FPE solvers by calculating unequal time joint PDFs. For the linear process with a linear damping force, joint PDF is found to be a Gaussian. In contrast, for the cubic process with a cubic damping force, joint PDF exhibits a bimodal structure, even in a stationary state. This suggests a finite memory time induced by a nonlinear force. Furthermore, several power-law scalings in the characteristics of bimodal PDFs are identified and investigated. Full article
(This article belongs to the Special Issue Entropies, Information Geometry and Fluctuations in Non-equilibrium Systems)
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16 pages, 5801 KiB  
Article
Pseudoclassical Dynamics of the Kicked Top
by Zhixing Zou and Jiao Wang
Entropy 2022, 24(8), 1092; https://doi.org/10.3390/e24081092 - 09 Aug 2022
Cited by 2 | Viewed by 1549
Abstract
The kicked rotor and the kicked top are two paradigms of quantum chaos. The notions of quantum resonance and the pseudoclassical limit, developed in the study of the kicked rotor, have revealed an intriguing and unconventional aspect of classical–quantum correspondence. Here, we show [...] Read more.
The kicked rotor and the kicked top are two paradigms of quantum chaos. The notions of quantum resonance and the pseudoclassical limit, developed in the study of the kicked rotor, have revealed an intriguing and unconventional aspect of classical–quantum correspondence. Here, we show that, by extending these notions to the kicked top, its rich dynamical behavior can be appreciated more thoroughly; of special interest is the entanglement entropy. In particular, the periodic synchronization between systems subject to different kicking strength can be conveniently understood and elaborated from the pseudoclassical perspective. The applicability of the suggested general pseudoclassical theory to the kicked rotor is also discussed. Full article
(This article belongs to the Special Issue Quantum Chaos—Dedicated to Professor Giulio Casati on the Occasion of His 80th Birthday)
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25 pages, 409 KiB  
Article
Information Theoretic Methods for Variable Selection—A Review
by Jan Mielniczuk
Entropy 2022, 24(8), 1079; https://doi.org/10.3390/e24081079 - 04 Aug 2022
Cited by 6 | Viewed by 1603
Abstract
We review the principal information theoretic tools and their use for feature selection, with the main emphasis on classification problems with discrete features. Since it is known that empirical versions of conditional mutual information perform poorly for high-dimensional problems, we focus on various [...] Read more.
We review the principal information theoretic tools and their use for feature selection, with the main emphasis on classification problems with discrete features. Since it is known that empirical versions of conditional mutual information perform poorly for high-dimensional problems, we focus on various ways of constructing its counterparts and the properties and limitations of such methods. We present a unified way of constructing such measures based on truncation, or truncation and weighing, for the Möbius expansion of conditional mutual information. We also discuss the main approaches to feature selection which apply the introduced measures of conditional dependence, together with the ways of assessing the quality of the obtained vector of predictors. This involves discussion of recent results on asymptotic distributions of empirical counterparts of criteria, as well as advances in resampling. Full article
(This article belongs to the Special Issue Information Theoretic Criteria: New Theoretical Developments and Applications)
6 pages, 255 KiB  
Article
Memory and Entropy
by Carlo Rovelli
Entropy 2022, 24(8), 1022; https://doi.org/10.3390/e24081022 - 24 Jul 2022
Cited by 3 | Viewed by 3931
Abstract
I study the physical nature of traces. Surprisingly, (i) systems separation with (ii) temperature differences and (iii) long thermalization times are sufficient conditions to produce macroscopic traces. Traces of the past are ubiquitous because these conditions are largely satisfied in our universe. I [...] Read more.
I study the physical nature of traces. Surprisingly, (i) systems separation with (ii) temperature differences and (iii) long thermalization times are sufficient conditions to produce macroscopic traces. Traces of the past are ubiquitous because these conditions are largely satisfied in our universe. I quantify these thermodynamical conditions for memory and derive an expression for the maximum amount of information stored in such memories as a function of the relevant thermodynamical parameters. This mechanism transforms low entropy into available information. I suggest that all macroscopic information has this origin in past low entropy. Full article
(This article belongs to the Special Issue The Ubiquity of Entropy II)
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11 pages, 4222 KiB  
Article
Critical Quantum Metrology in the Non-Linear Quantum Rabi Model
by Zu-Jian Ying, Simone Felicetti, Gang Liu and Daniel Braak
Entropy 2022, 24(8), 1015; https://doi.org/10.3390/e24081015 - 22 Jul 2022
Cited by 18 | Viewed by 2027
Abstract
The quantum Rabi model (QRM) with linear coupling between light mode and qubit exhibits the analog of a second-order phase transition for vanishing mode frequency which allows for criticality-enhanced quantum metrology in a few-body system. We show that the QRM including a nonlinear [...] Read more.
The quantum Rabi model (QRM) with linear coupling between light mode and qubit exhibits the analog of a second-order phase transition for vanishing mode frequency which allows for criticality-enhanced quantum metrology in a few-body system. We show that the QRM including a nonlinear coupling term exhibits much higher measurement precisions due to its first-order-like phase transition at finite frequency, avoiding the detrimental slowing-down effect close to the critical point of the linear QRM. When a bias term is added to the Hamiltonian, the system can be used as a fluxmeter or magnetometer if implemented in circuit QED platforms. Full article
(This article belongs to the Special Issue Current Trends in Quantum Phase Transitions)
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15 pages, 14830 KiB  
Article
Consensus, Polarization and Hysteresis in the Three-State Noisy q-Voter Model with Bounded Confidence
by Maciej Doniec, Arkadiusz Lipiecki and Katarzyna Sznajd-Weron
Entropy 2022, 24(7), 983; https://doi.org/10.3390/e24070983 - 16 Jul 2022
Cited by 7 | Viewed by 1605
Abstract
In this work, we address the question of the role of the influence of group size on the emergence of various collective social phenomena, such as consensus, polarization and social hysteresis. To answer this question, we study the three-state noisy q-voter model [...] Read more.
In this work, we address the question of the role of the influence of group size on the emergence of various collective social phenomena, such as consensus, polarization and social hysteresis. To answer this question, we study the three-state noisy q-voter model with bounded confidence, in which agents can be in one of three states: two extremes (leftist and rightist) and centrist. We study the model on a complete graph within the mean-field approach and show that, depending on the size q of the influence group, saddle-node bifurcation cascades of different length appear and different collective phenomena are possible. In particular, for all values of q>1, social hysteresis is observed. Furthermore, for small values of q∈(1,4), disagreement, polarization and domination of centrists (a consensus understood as the general agreement, not unanimity) can be achieved but not the domination of extremists. The latter is possible only for larger groups of influence. Finally, by comparing our model to others, we discuss how a small change in the rules at the microscopic level can dramatically change the macroscopic behavior of the model. Full article
(This article belongs to the Special Issue Modern Trends in Sociophysics)
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19 pages, 2088 KiB  
Review
Revealing the Dynamics of Neural Information Processing with Multivariate Information Decomposition
by Ehren L. Newman, Thomas F. Varley, Vibin K. Parakkattu, Samantha P. Sherrill and John M. Beggs
Entropy 2022, 24(7), 930; https://doi.org/10.3390/e24070930 - 05 Jul 2022
Cited by 8 | Viewed by 3120
Abstract
The varied cognitive abilities and rich adaptive behaviors enabled by the animal nervous system are often described in terms of information processing. This framing raises the issue of how biological neural circuits actually process information, and some of the most fundamental outstanding questions [...] Read more.
The varied cognitive abilities and rich adaptive behaviors enabled by the animal nervous system are often described in terms of information processing. This framing raises the issue of how biological neural circuits actually process information, and some of the most fundamental outstanding questions in neuroscience center on understanding the mechanisms of neural information processing. Classical information theory has long been understood to be a natural framework within which information processing can be understood, and recent advances in the field of multivariate information theory offer new insights into the structure of computation in complex systems. In this review, we provide an introduction to the conceptual and practical issues associated with using multivariate information theory to analyze information processing in neural circuits, as well as discussing recent empirical work in this vein. Specifically, we provide an accessible introduction to the partial information decomposition (PID) framework. PID reveals redundant, unique, and synergistic modes by which neurons integrate information from multiple sources. We focus particularly on the synergistic mode, which quantifies the “higher-order” information carried in the patterns of multiple inputs and is not reducible to input from any single source. Recent work in a variety of model systems has revealed that synergistic dynamics are ubiquitous in neural circuitry and show reliable structure–function relationships, emerging disproportionately in neuronal rich clubs, downstream of recurrent connectivity, and in the convergence of correlated activity. We draw on the existing literature on higher-order information dynamics in neuronal networks to illustrate the insights that have been gained by taking an information decomposition perspective on neural activity. Finally, we briefly discuss future promising directions for information decomposition approaches to neuroscience, such as work on behaving animals, multi-target generalizations of PID, and time-resolved local analyses. Full article
(This article belongs to the Special Issue Information Theory in Computational Biology)
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32 pages, 18172 KiB  
Article
Causal Inference in Time Series in Terms of Rényi Transfer Entropy
by Petr Jizba, Hynek Lavička and Zlata Tabachová
Entropy 2022, 24(7), 855; https://doi.org/10.3390/e24070855 - 22 Jun 2022
Cited by 4 | Viewed by 2772
Abstract
Uncovering causal interdependencies from observational data is one of the great challenges of a nonlinear time series analysis. In this paper, we discuss this topic with the help of an information-theoretic concept known as Rényi’s information measure. In particular, we tackle the directional [...] Read more.
Uncovering causal interdependencies from observational data is one of the great challenges of a nonlinear time series analysis. In this paper, we discuss this topic with the help of an information-theoretic concept known as Rényi’s information measure. In particular, we tackle the directional information flow between bivariate time series in terms of Rényi’s transfer entropy. We show that by choosing Rényi’s parameter α, we can appropriately control information that is transferred only between selected parts of the underlying distributions. This, in turn, is a particularly potent tool for quantifying causal interdependencies in time series, where the knowledge of “black swan” events, such as spikes or sudden jumps, are of key importance. In this connection, we first prove that for Gaussian variables, Granger causality and Rényi transfer entropy are entirely equivalent. Moreover, we also partially extend these results to heavy-tailed α-Gaussian variables. These results allow establishing a connection between autoregressive and Rényi entropy-based information-theoretic approaches to data-driven causal inference. To aid our intuition, we employed the Leonenko et al. entropy estimator and analyzed Rényi’s information flow between bivariate time series generated from two unidirectionally coupled Rössler systems. Notably, we find that Rényi’s transfer entropy not only allows us to detect a threshold of synchronization but it also provides non-trivial insight into the structure of a transient regime that exists between the region of chaotic correlations and synchronization threshold. In addition, from Rényi’s transfer entropy, we could reliably infer the direction of coupling and, hence, causality, only for coupling strengths smaller than the onset value of the transient regime, i.e., when two Rössler systems are coupled but have not yet entered synchronization. Full article
(This article belongs to the Special Issue Entropy-Based Applications in Economics, Finance, and Management)
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14 pages, 471 KiB  
Article
Multi-User Measurement-Device-Independent Quantum Key Distribution Based on GHZ Entangled State
by Ximing Hua, Min Hu and Banghong Guo
Entropy 2022, 24(6), 841; https://doi.org/10.3390/e24060841 - 18 Jun 2022
Cited by 7 | Viewed by 1838
Abstract
As a multi-particle entangled state, the Greenberger–Horne–Zeilinger (GHZ) state plays an important role in quantum theory and applications. In this study, we propose a flexible multi-user measurement-device-independent quantum key distribution (MDI-QKD) scheme based on a GHZ entangled state. Our scheme can distribute quantum [...] Read more.
As a multi-particle entangled state, the Greenberger–Horne–Zeilinger (GHZ) state plays an important role in quantum theory and applications. In this study, we propose a flexible multi-user measurement-device-independent quantum key distribution (MDI-QKD) scheme based on a GHZ entangled state. Our scheme can distribute quantum keys among multiple users while being resistant to detection attacks. Our simulation results show that the secure distance between each user and the measurement device can reach more than 280 km while reducing the complexity of the quantum network. Additionally, we propose a method to expand our scheme to a multi-node with multi-user network, which can further enhance the communication distance between the users at different nodes. Full article
(This article belongs to the Special Issue Quantum Information and Computation)
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28 pages, 1093 KiB  
Article
Effective Field Theory of Random Quantum Circuits
by Yunxiang Liao and Victor Galitski
Entropy 2022, 24(6), 823; https://doi.org/10.3390/e24060823 - 13 Jun 2022
Cited by 2 | Viewed by 2097
Abstract
Quantum circuits have been widely used as a platform to simulate generic quantum many-body systems. In particular, random quantum circuits provide a means to probe universal features of many-body quantum chaos and ergodicity. Some such features have already been experimentally demonstrated in noisy [...] Read more.
Quantum circuits have been widely used as a platform to simulate generic quantum many-body systems. In particular, random quantum circuits provide a means to probe universal features of many-body quantum chaos and ergodicity. Some such features have already been experimentally demonstrated in noisy intermediate-scale quantum (NISQ) devices. On the theory side, properties of random quantum circuits have been studied on a case-by-case basis and for certain specific systems, and a hallmark of quantum chaos—universal Wigner–Dyson level statistics—has been derived. This work develops an effective field theory for a large class of random quantum circuits. The theory has the form of a replica sigma model and is similar to the low-energy approach to diffusion in disordered systems. The method is used to explicitly derive the universal random matrix behavior of a large family of random circuits. In particular, we rederive the Wigner–Dyson spectral statistics of the brickwork circuit model by Chan, De Luca, and Chalker [Phys. Rev. X 8, 041019 (2018)] and show within the same calculation that its various permutations and higher-dimensional generalizations preserve the universal level statistics. Finally, we use the replica sigma model framework to rederive the Weingarten calculus, which is a method of evaluating integrals of polynomials of matrix elements with respect to the Haar measure over compact groups and has many applications in the study of quantum circuits. The effective field theory derived here provides both a method to quantitatively characterize the quantum dynamics of random Floquet systems (e.g., calculating operator and entanglement spreading) and a path to understanding the general fundamental mechanism behind quantum chaos and thermalization in these systems. Full article
(This article belongs to the Special Issue Quantum Chaos—Dedicated to Professor Giulio Casati on the Occasion of His 80th Birthday)
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17 pages, 443 KiB  
Article
Quantum Non-Markovian Environment-to-System Backflows of Information: Nonoperational vs. Operational Approaches
by Adrián A. Budini
Entropy 2022, 24(5), 649; https://doi.org/10.3390/e24050649 - 05 May 2022
Cited by 8 | Viewed by 1460
Abstract
Quantum memory effects can be qualitatively understood as a consequence of an environment-to-system backflow of information. Here, we analyze and compare how this concept is interpreted and implemented in different approaches to quantum non-Markovianity. We study a nonoperational approach, defined by the distinguishability [...] Read more.
Quantum memory effects can be qualitatively understood as a consequence of an environment-to-system backflow of information. Here, we analyze and compare how this concept is interpreted and implemented in different approaches to quantum non-Markovianity. We study a nonoperational approach, defined by the distinguishability between two system states characterized by different initial conditions, and an operational approach, which is defined by the correlation between different outcomes associated to successive measurement processes performed over the system of interest. The differences, limitations, and vantages of each approach are characterized in detail by considering diverse system–environment models and dynamics. As a specific example, we study a non-Markovian depolarizing map induced by the interaction of the system of interest with an environment characterized by incoherent and coherent self-dynamics. Full article
(This article belongs to the Special Issue Quantum Information Concepts in Open Quantum Systems)
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44 pages, 2198 KiB  
Article
Entropy and the Experience of Heat
by Hans U. Fuchs, Michele D’Anna and Federico Corni
Entropy 2022, 24(5), 646; https://doi.org/10.3390/e24050646 - 04 May 2022
Cited by 5 | Viewed by 2108
Abstract
We discuss how to construct a direct and experientially natural path to entropy as a extensive quantity of a macroscopic theory of thermal systems and processes. The scientific aspects of this approach are based upon continuum thermodynamics. We ask what the roots of [...] Read more.
We discuss how to construct a direct and experientially natural path to entropy as a extensive quantity of a macroscopic theory of thermal systems and processes. The scientific aspects of this approach are based upon continuum thermodynamics. We ask what the roots of an experientially natural approach might be—to this end we investigate and describe in some detail (a) how humans experience and conceptualize an extensive thermal quantity (i.e., an amount of heat), and (b) how this concept evolved during the early development of the science of thermal phenomena (beginning with the Experimenters of the Accademia del Cimento and ending with Sadi Carnot). We show that a direct approach to entropy, as the extensive quantity of models of thermal systems and processes, is possible and how it can be applied to the teaching of thermodynamics for various audiences. Full article
(This article belongs to the Special Issue Nature of Entropy and Its Direct Metrology)
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32 pages, 10388 KiB  
Article
The Cross-Sectional Intrinsic Entropy—A Comprehensive Stock Market Volatility Estimator
by Claudiu Vințe and Marcel Ausloos
Entropy 2022, 24(5), 623; https://doi.org/10.3390/e24050623 - 29 Apr 2022
Cited by 4 | Viewed by 2823
Abstract
To take into account the temporal dimension of uncertainty in stock markets, this paper introduces a cross-sectional estimation of stock market volatility based on the intrinsic entropy model. The proposed cross-sectional intrinsic entropy (CSIE) is defined and computed as a daily [...] Read more.
To take into account the temporal dimension of uncertainty in stock markets, this paper introduces a cross-sectional estimation of stock market volatility based on the intrinsic entropy model. The proposed cross-sectional intrinsic entropy (CSIE) is defined and computed as a daily volatility estimate for the entire market, grounded on the daily traded prices—open, high, low, and close prices (OHLC)—along with the daily traded volume for all symbols listed on The New York Stock Exchange (NYSE) and The National Association of Securities Dealers Automated Quotations (NASDAQ). We perform a comparative analysis between the time series obtained from the CSIE and the historical volatility as provided by the estimators: close-to-close, Parkinson, Garman–Klass, Rogers–Satchell, Yang–Zhang, and intrinsic entropy (IE), defined and computed from historical OHLC daily prices of the Standard & Poor’s 500 index (S&P500), Dow Jones Industrial Average (DJIA), and the NASDAQ Composite index, respectively, for various time intervals. Our study uses an approximate 6000-day reference point, starting 1 January 2001, until 23 January 2022, for both the NYSE and the NASDAQ. We found that the CSIE market volatility estimator is consistently at least 10 times more sensitive to market changes, compared to the volatility estimate captured through the market indices. Furthermore, beta values confirm a consistently lower volatility risk for market indices overall, between 50% and 90% lower, compared to the volatility risk of the entire market in various time intervals and rolling windows. Full article
(This article belongs to the Special Issue Fractal and Multifractal Analysis of Complex Networks)
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28 pages, 514 KiB  
Article
Robust Test Statistics Based on Restricted Minimum Rényi’s Pseudodistance Estimators
by María Jaenada, Pedro Miranda and Leandro Pardo
Entropy 2022, 24(5), 616; https://doi.org/10.3390/e24050616 - 28 Apr 2022
Cited by 5 | Viewed by 1382
Abstract
The Rao’s score, Wald and likelihood ratio tests are the most common procedures for testing hypotheses in parametric models. None of the three test statistics is uniformly superior to the other two in relation with the power function, and moreover, they are first-order [...] Read more.
The Rao’s score, Wald and likelihood ratio tests are the most common procedures for testing hypotheses in parametric models. None of the three test statistics is uniformly superior to the other two in relation with the power function, and moreover, they are first-order equivalent and asymptotically optimal. Conversely, these three classical tests present serious robustness problems, as they are based on the maximum likelihood estimator, which is highly non-robust. To overcome this drawback, some test statistics have been introduced in the literature based on robust estimators, such as robust generalized Wald-type and Rao-type tests based on minimum divergence estimators. In this paper, restricted minimum Rényi’s pseudodistance estimators are defined, and their asymptotic distribution and influence function are derived. Further, robust Rao-type and divergence-based tests based on minimum Rényi’s pseudodistance and restricted minimum Rényi’s pseudodistance estimators are considered, and the asymptotic properties of the new families of tests statistics are obtained. Finally, the robustness of the proposed estimators and test statistics is empirically examined through a simulation study, and illustrative applications in real-life data are analyzed. Full article
(This article belongs to the Special Issue Information and Divergence Measures)
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26 pages, 2272 KiB  
Article
Metacognition as a Consequence of Competing Evolutionary Time Scales
by Franz Kuchling, Chris Fields and Michael Levin
Entropy 2022, 24(5), 601; https://doi.org/10.3390/e24050601 - 26 Apr 2022
Cited by 11 | Viewed by 6505
Abstract
Evolution is full of coevolving systems characterized by complex spatio-temporal interactions that lead to intertwined processes of adaptation. Yet, how adaptation across multiple levels of temporal scales and biological complexity is achieved remains unclear. Here, we formalize how evolutionary multi-scale processing underlying adaptation [...] Read more.
Evolution is full of coevolving systems characterized by complex spatio-temporal interactions that lead to intertwined processes of adaptation. Yet, how adaptation across multiple levels of temporal scales and biological complexity is achieved remains unclear. Here, we formalize how evolutionary multi-scale processing underlying adaptation constitutes a form of metacognition flowing from definitions of metaprocessing in machine learning. We show (1) how the evolution of metacognitive systems can be expected when fitness landscapes vary on multiple time scales, and (2) how multiple time scales emerge during coevolutionary processes of sufficiently complex interactions. After defining a metaprocessor as a regulator with local memory, we prove that metacognition is more energetically efficient than purely object-level cognition when selection operates at multiple timescales in evolution. Furthermore, we show that existing modeling approaches to coadaptation and coevolution—here active inference networks, predator–prey interactions, coupled genetic algorithms, and generative adversarial networks—lead to multiple emergent timescales underlying forms of metacognition. Lastly, we show how coarse-grained structures emerge naturally in any resource-limited system, providing sufficient evidence for metacognitive systems to be a prevalent and vital component of (co-)evolution. Therefore, multi-scale processing is a necessary requirement for many evolutionary scenarios, leading to de facto metacognitive evolutionary outcomes. Full article
(This article belongs to the Special Issue Towards a Quantitative Understanding of Agency)
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31 pages, 469 KiB  
Article
Information Inequalities via Submodularity and a Problem in Extremal Graph Theory
by Igal Sason
Entropy 2022, 24(5), 597; https://doi.org/10.3390/e24050597 - 25 Apr 2022
Cited by 3 | Viewed by 2303
Abstract
The present paper offers, in its first part, a unified approach for the derivation of families of inequalities for set functions which satisfy sub/supermodularity properties. It applies this approach for the derivation of information inequalities with Shannon information measures. Connections of the considered [...] Read more.
The present paper offers, in its first part, a unified approach for the derivation of families of inequalities for set functions which satisfy sub/supermodularity properties. It applies this approach for the derivation of information inequalities with Shannon information measures. Connections of the considered approach to a generalized version of Shearer’s lemma, and other related results in the literature are considered. Some of the derived information inequalities are new, and also known results (such as a generalized version of Han’s inequality) are reproduced in a simple and unified way. In its second part, this paper applies the generalized Han’s inequality to analyze a problem in extremal graph theory. This problem is motivated and analyzed from the perspective of information theory, and the analysis leads to generalized and refined bounds. The two parts of this paper are meant to be independently accessible to the reader. Full article
(This article belongs to the Special Issue Information and Divergence Measures)
20 pages, 309 KiB  
Article
Quantum Gravity If Non-Locality Is Fundamental
by Stuart A. Kauffman
Entropy 2022, 24(4), 554; https://doi.org/10.3390/e24040554 - 15 Apr 2022
Cited by 6 | Viewed by 2354
Abstract
I take non-locality to be the Michelson–Morley experiment of the early 21st century, assume its universal validity, and try to derive its consequences. Spacetime, with its locality, cannot be fundamental, but must somehow be emergent from entangled coherent quantum variables and their behaviors. [...] Read more.
I take non-locality to be the Michelson–Morley experiment of the early 21st century, assume its universal validity, and try to derive its consequences. Spacetime, with its locality, cannot be fundamental, but must somehow be emergent from entangled coherent quantum variables and their behaviors. There are, then, two immediate consequences: (i). if we start with non-locality, we need not explain non-locality. We must instead explain an emergence of locality and spacetime. (ii). There can be no emergence of spacetime without matter. These propositions flatly contradict General Relativity, which is foundationally local, can be formulated without matter, and in which there is no “emergence” of spacetime. If these be true, then quantum gravity cannot be a minor alteration of General Relativity but must demand its deep reformulation. This will almost inevitably lead to: matter not only curves spacetime, but “creates” spacetime. We will see independent grounds for the assertion that matter both curves and creates spacetime that may invite a new union of quantum gravity and General Relativity. This quantum creation of spacetime consists of: (i) fully non-local entangled coherent quantum variables. (ii) The onset of locality via decoherence. (iii) A metric in Hilbert space among entangled quantum variables by the sub-additive von Neumann entropy between pairs of variables. (iv) Mapping from metric distances in Hilbert space to metric distances in classical spacetime by episodic actualization events. (v) Discrete spacetime is the relations among these discrete actualization events. (vi) “Now” is the shared moment of actualization of one among the entangled variables when the amplitudes of the remaining entangled variables change instantaneously. (vii) The discrete, successive, episodic, irreversible actualization events constitute a quantum arrow of time. (viii) The arrow of time history of these events is recorded in the very structure of the spacetime constructed. (ix) Actual Time is a succession of two or more actual events. The theory inevitably yields a UV cutoff of a new type. The cutoff is a phase transition between continuous spacetime before the transition and discontinuous spacetime beyond the phase transition. This quantum creation of spacetime modifies General Relativity and may account for Dark Energy, Dark Matter, and the possible elimination of the singularities of General Relativity. Relations to Causal Set Theory, faithful Lorentzian manifolds, and past and future light cones joined at “Actual Now” are discussed. Possible observational and experimental tests based on: (i). the existence of Sub- Planckian photons, (ii). knee and ankle discontinuities in the high-energy gamma ray spectrum, and (iii). possible experiments to detect a creation of spacetime in the Casimir system are discussed. A quantum actualization enhancement of repulsive Casimir effect would be anti-gravitational and of possible practical use. The ideas and concepts discussed here are not yet a theory, but at most the start of a framework that may be useful. Full article
18 pages, 12693 KiB  
Article
Recasting the (Synchrosqueezed) Short-Time Fourier Transform as an Instantaneous Spectrum
by Steven Sandoval and Phillip L. De Leon
Entropy 2022, 24(4), 518; https://doi.org/10.3390/e24040518 - 06 Apr 2022
Cited by 7 | Viewed by 1797
Abstract
In a previous work, we proposed a time-frequency analysis called instantaneous spectral analysis (ISA), which generalizes the notion of the Fourier spectrum and in which instantaneous frequency is utilized to the fullest extent. In this paper, we recast both the Fourier transform (FT) [...] Read more.
In a previous work, we proposed a time-frequency analysis called instantaneous spectral analysis (ISA), which generalizes the notion of the Fourier spectrum and in which instantaneous frequency is utilized to the fullest extent. In this paper, we recast both the Fourier transform (FT) and filterbank (FB) interpretations of the short-time Fourier transform (STFT) as instantaneous spectra. We show that to recast the FB interpretation of STFT as an instantaneous spectrum with valid structure, frequency reassignment is a fundamental necessity, thus demonstrating that this IS is closely related to the synchrosqueezed STFT. This result provides a new theoretical motivation for the synchrosqueezed STFT. Finally, we illustrate through example the instantaneous spectra corresponding to the FT and FB interpretations of STFT using two closed-form examples. Full article
(This article belongs to the Special Issue Time-Frequency Analysis, AM-FM Models, and Mode Decompositions)
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22 pages, 741 KiB  
Article
Quantum Coherences and Classical Inhomogeneities as Equivalent Thermodynamics Resources
by Andrew Smith, Kanupriya Sinha and Christopher Jarzynski
Entropy 2022, 24(4), 474; https://doi.org/10.3390/e24040474 - 29 Mar 2022
Cited by 5 | Viewed by 4405
Abstract
Quantum energy coherences represent a thermodynamic resource, which can be exploited to extract energy from a thermal reservoir and deliver that energy as work. We argue that there exists a closely analogous classical thermodynamic resource, namely, energy-shell inhomogeneities in the phase space distribution [...] Read more.
Quantum energy coherences represent a thermodynamic resource, which can be exploited to extract energy from a thermal reservoir and deliver that energy as work. We argue that there exists a closely analogous classical thermodynamic resource, namely, energy-shell inhomogeneities in the phase space distribution of a system’s initial state. We compare the amount of work that can be obtained from quantum coherences with the amount that can be obtained from classical inhomogeneities, and find them to be equal in the semiclassical limit. We thus conclude that coherences do not provide a unique thermodynamic advantage of quantum systems over classical systems, in situations where a well-defined semiclassical correspondence exists. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
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