Next Issue
Volume 26, April
Previous Issue
Volume 26, February
 
 
entropy-logo

Journal Browser

Journal Browser

Entropy, Volume 26, Issue 3 (March 2024) – 100 articles

Cover Story (view full-size image): Symmetry breaking, observed from the early universe to complex organisms, remains a key puzzle in understanding life’s emergence. The origin, particularly from an energetic standpoint, remains unexplained. Our novel approach considers energy dissipation crucial in elucidating symmetry breaking, particularly lost free energy. Through comprehensive thermodynamic analysis across scales, we present experimental evidence and establish a direct link between nonequilibrium free energy and energy dissipation during structure formation. Results highlight energy dissipation’s pivotal role, not just as an outcome, but as the trigger for symmetry breaking. This insight suggests that understanding complex systems’ origins requires focusing on nonequilibrium processes. View this paper
  • Issues are regarded as officially published after their release is announced to the table of contents alert mailing list.
  • You may sign up for e-mail alerts to receive table of contents of newly released issues.
  • PDF is the official format for papers published in both, html and pdf forms. To view the papers in pdf format, click on the "PDF Full-text" link, and use the free Adobe Reader to open them.
Order results
Result details
Section
Select all
Export citation of selected articles as:
12 pages, 794 KiB  
Article
Weak Scale Supersymmetry Emergent from the String Landscape
by Howard Baer, Vernon Barger, Dakotah Martinez and Shadman Salam
Entropy 2024, 26(3), 275; https://doi.org/10.3390/e26030275 - 21 Mar 2024
Cited by 1 | Viewed by 494
Abstract
Superstring flux compactifications can stabilize all moduli while leading to an enormous number of vacua solutions, each leading to different 4d laws of physics. While the string landscape provides at present the only plausible explanation for the size of the cosmological [...] Read more.
Superstring flux compactifications can stabilize all moduli while leading to an enormous number of vacua solutions, each leading to different 4d laws of physics. While the string landscape provides at present the only plausible explanation for the size of the cosmological constant, it may also predict the form of weak scale supersymmetry which is expected to emerge. Rather general arguments suggest a power-law draw to large soft terms, but these are subject to an anthropic selection of a not-too-large value for the weak scale. The combined selection allows one to compute relative probabilities for the emergence of supersymmetric models from the landscape. Models with weak scale naturalness appear most likely to emerge since they have the largest parameter space on the landscape. For finetuned models such as high-scale SUSY or split SUSY, the required weak scale finetuning shrinks their parameter space to tiny volumes, making them much less likely to appear compared to natural models. Probability distributions for sparticle and Higgs masses from natural models show a preference for Higgs mass mh125 GeV, with sparticles typically beyond the present LHC limits, in accord with data. From these considerations, we briefly describe how natural SUSY is expected to be revealed at future LHC upgrades. This article is a contribution to the Special Edition of the journal Entropy, honoring Paul Frampton on his 80th birthday. Full article
Show Figures

Figure 1

8 pages, 886 KiB  
Article
Hyper-Ballistic Superdiffusion of Competing Microswimmers
by Kristian Stølevik Olsen, Alex Hansen and Eirik Grude Flekkøy
Entropy 2024, 26(3), 274; https://doi.org/10.3390/e26030274 - 21 Mar 2024
Viewed by 583
Abstract
Hyper-ballistic diffusion is shown to arise from a simple model of microswimmers moving through a porous media while competing for resources. By using a mean-field model where swimmers interact through the local concentration, we show that a non-linear Fokker–Planck equation arises. The solution [...] Read more.
Hyper-ballistic diffusion is shown to arise from a simple model of microswimmers moving through a porous media while competing for resources. By using a mean-field model where swimmers interact through the local concentration, we show that a non-linear Fokker–Planck equation arises. The solution exhibits hyper-ballistic superdiffusive motion, with a diffusion exponent of four. A microscopic simulation strategy is proposed, which shows excellent agreement with theoretical analysis. Full article
(This article belongs to the Special Issue Statistical Mechanics of Porous Media Flow)
Show Figures

Figure 1

12 pages, 456 KiB  
Article
Tsallis Distribution as a Λ-Deformation of the Maxwell–Jüttner Distribution
by Jean-Pierre Gazeau
Entropy 2024, 26(3), 273; https://doi.org/10.3390/e26030273 - 21 Mar 2024
Viewed by 511
Abstract
Currently, there is no widely accepted consensus regarding a consistent thermodynamic framework within the special relativity paradigm. However, by postulating that the inverse temperature 4-vector, denoted as β, is future-directed and time-like, intriguing insights emerge. Specifically, it is demonstrated that the q [...] Read more.
Currently, there is no widely accepted consensus regarding a consistent thermodynamic framework within the special relativity paradigm. However, by postulating that the inverse temperature 4-vector, denoted as β, is future-directed and time-like, intriguing insights emerge. Specifically, it is demonstrated that the q-dependent Tsallis distribution can be conceptualized as a de Sitterian deformation of the relativistic Maxwell–Jüttner distribution. In this context, the curvature of the de Sitter space-time is characterized by Λ/3, where Λ represents the cosmological constant within the ΛCDM standard model for cosmology. For a simple gas composed of particles with proper mass m, and within the framework of quantum statistical de Sitterian considerations, the Tsallis parameter q exhibits a dependence on the cosmological constant given by q=1+cΛ/n, where c=/mc is the Compton length of the particle and n is a positive numerical factor, the determination of which awaits observational confirmation. This formulation establishes a novel connection between the Tsallis distribution, quantum statistics, and the cosmological constant, shedding light on the intricate interplay between relativistic thermodynamics and fundamental cosmological parameters. Full article
Show Figures

Figure 1

18 pages, 7149 KiB  
Article
Entanglement Phase Transitions in Non-Hermitian Kitaev Chains
by Longwen Zhou
Entropy 2024, 26(3), 272; https://doi.org/10.3390/e26030272 - 20 Mar 2024
Viewed by 570
Abstract
The intricate interplay between unitary evolution and projective measurements could induce entanglement phase transitions in the nonequilibrium dynamics of quantum many-particle systems. In this work, we uncover loss-induced entanglement transitions in non-Hermitian topological superconductors. In prototypical Kitaev chains with onsite particle losses and [...] Read more.
The intricate interplay between unitary evolution and projective measurements could induce entanglement phase transitions in the nonequilibrium dynamics of quantum many-particle systems. In this work, we uncover loss-induced entanglement transitions in non-Hermitian topological superconductors. In prototypical Kitaev chains with onsite particle losses and varying hopping and pairing ranges, the bipartite entanglement entropy of steady states is found to scale logarithmically versus the system size in topologically nontrivial phases and become independent of the system size in the trivial phase. Notably, the scaling coefficients of log-law entangled phases are distinguishable when the underlying system resides in different topological phases. Log-law to log-law and log-law to area-law entanglement phase transitions are further identified when the system switches between different topological phases and goes from a topologically nontrivial to a trivial phase, respectively. These findings not only establish the relationships among spectral, topological and entanglement properties in a class of non-Hermitian topological superconductors but also provide an efficient means to dynamically reveal their distinctive topological features. Full article
(This article belongs to the Special Issue Entanglement Entropy and Quantum Phase Transition)
Show Figures

Figure 1

24 pages, 790 KiB  
Article
A Measure of Synergy Based on Union Information
by André F. C. Gomes and Mário A. T. Figueiredo
Entropy 2024, 26(3), 271; https://doi.org/10.3390/e26030271 - 19 Mar 2024
Viewed by 655
Abstract
The partial information decomposition (PID) framework is concerned with decomposing the information that a set of (two or more) random variables (the sources) has about another variable (the target) into three types of information: unique, redundant, and synergistic. Classical information theory alone does [...] Read more.
The partial information decomposition (PID) framework is concerned with decomposing the information that a set of (two or more) random variables (the sources) has about another variable (the target) into three types of information: unique, redundant, and synergistic. Classical information theory alone does not provide a unique way to decompose information in this manner and additional assumptions have to be made. One often overlooked way to achieve this decomposition is using a so-called measure of union information—which quantifies the information that is present in at least one of the sources—from which a synergy measure stems. In this paper, we introduce a new measure of union information based on adopting a communication channel perspective, compare it with existing measures, and study some of its properties. We also include a comprehensive critical review of characterizations of union information and synergy measures that have been proposed in the literature. Full article
Show Figures

Figure 1

14 pages, 12048 KiB  
Article
Decoding the News Media Diet of Disinformation Spreaders
by Anna Bertani, Valeria Mazzeo and Riccardo Gallotti
Entropy 2024, 26(3), 270; https://doi.org/10.3390/e26030270 - 19 Mar 2024
Viewed by 584
Abstract
In the digital era, information consumption is predominantly channeled through online news media and disseminated on social media platforms. Understanding the complex dynamics of the news media environment and users’ habits within the digital ecosystem is a challenging task that requires, at the [...] Read more.
In the digital era, information consumption is predominantly channeled through online news media and disseminated on social media platforms. Understanding the complex dynamics of the news media environment and users’ habits within the digital ecosystem is a challenging task that requires, at the same time, large databases and accurate methodological approaches. This study contributes to this expanding research landscape by employing network science methodologies and entropic measures to analyze the behavioral patterns of social media users sharing news pieces and dig into the diverse news consumption habits within different online social media user groups. Our analyses reveal that users are more inclined to share news classified as fake when they have previously posted conspiracy or junk science content and vice versa, creating a series of “misinformation hot streaks”. To better understand these dynamics, we used three different measures of entropy to gain insights into the news media habits of each user, finding that the patterns of news consumption significantly differ among users when focusing on disinformation spreaders as opposed to accounts sharing reliable or low-risk content. Thanks to these entropic measures, we quantify the variety and the regularity of the news media diet, finding that those disseminating unreliable content exhibit a more varied and, at the same time, a more regular choice of web-domains. This quantitative insight into the nuances of news consumption behaviors exhibited by disinformation spreaders holds the potential to significantly inform the strategic formulation of more robust and adaptive social media moderation policies. Full article
(This article belongs to the Special Issue Entropy-Based Applications in Sociophysics)
Show Figures

Figure 1

16 pages, 15509 KiB  
Article
HAG-NET: Hiding Data and Adversarial Attacking with Generative Adversarial Network
by Haiju Fan and Jinsong Wang
Entropy 2024, 26(3), 269; https://doi.org/10.3390/e26030269 - 19 Mar 2024
Viewed by 584
Abstract
Recent studies on watermarking techniques based on image carriers have demonstrated new approaches that combine adversarial perturbations against steganalysis with embedding distortions. However, while these methods successfully counter convolutional neural network-based steganalysis, they do not adequately protect the data of the carrier itself. [...] Read more.
Recent studies on watermarking techniques based on image carriers have demonstrated new approaches that combine adversarial perturbations against steganalysis with embedding distortions. However, while these methods successfully counter convolutional neural network-based steganalysis, they do not adequately protect the data of the carrier itself. Recognizing the high sensitivity of Deep Neural Networks (DNNs) to small perturbations, we propose HAG-NET, a method based on image carriers, which is jointly trained by the encoder, decoder, and attacker. In this paper, the encoder generates Adversarial Steganographic Examples (ASEs) that are adversarial to the target classification network, thereby providing protection for the carrier data. Additionally, the decoder can recover secret data from ASEs. The experimental results demonstrate that ASEs produced by HAG-NET achieve an average success rate of over 99% on both the MNIST and CIFAR-10 datasets. ASEs generated with the attacker exhibit greater robustness in terms of attack ability, with an average increase of about 3.32%. Furthermore, our method, when compared with other generative stego examples under similar perturbation strength, contains significantly more information according to image information entropy measurements. Full article
(This article belongs to the Topic Computational Complex Networks)
Show Figures

Figure 1

25 pages, 407 KiB  
Article
Game Theoretic Clustering for Finding Strong Communities
by Chao Zhao, Ali Al-Bashabsheh and Chung Chan
Entropy 2024, 26(3), 268; https://doi.org/10.3390/e26030268 - 18 Mar 2024
Viewed by 613
Abstract
We address the challenge of identifying meaningful communities by proposing a model based on convex game theory and a measure of community strength. Many existing community detection methods fail to provide unique solutions, and it remains unclear how the solutions depend on initial [...] Read more.
We address the challenge of identifying meaningful communities by proposing a model based on convex game theory and a measure of community strength. Many existing community detection methods fail to provide unique solutions, and it remains unclear how the solutions depend on initial conditions. Our approach identifies strong communities with a hierarchical structure, visualizable as a dendrogram, and computable in polynomial time using submodular function minimization. This framework extends beyond graphs to hypergraphs or even polymatroids. In the case when the model is graphical, a more efficient algorithm based on the max-flow min-cut algorithm can be devised. Though not achieving near-linear time complexity, the pursuit of practical algorithms is an intriguing avenue for future research. Our work serves as the foundation, offering an analytical framework that yields unique solutions with clear operational meaning for the communities identified. Full article
Show Figures

Figure 1

8 pages, 218 KiB  
Article
(Re)Construction of Quantum Space-Time: Transcribing Hilbert into Configuration Space
by Karl Svozil
Entropy 2024, 26(3), 267; https://doi.org/10.3390/e26030267 - 18 Mar 2024
Viewed by 552
Abstract
Space-time in quantum mechanics is about bridging Hilbert and configuration space. Thereby, an entirely new perspective is obtained by replacing the Newtonian space-time theater with the image of a presumably high-dimensional Hilbert space, through which space-time becomes an epiphenomenon construed by internal observers. [...] Read more.
Space-time in quantum mechanics is about bridging Hilbert and configuration space. Thereby, an entirely new perspective is obtained by replacing the Newtonian space-time theater with the image of a presumably high-dimensional Hilbert space, through which space-time becomes an epiphenomenon construed by internal observers. Full article
13 pages, 281 KiB  
Article
Group Structure as a Foundation for Entropies
by Henrik Jeldtoft Jensen and Piergiulio Tempesta
Entropy 2024, 26(3), 266; https://doi.org/10.3390/e26030266 - 18 Mar 2024
Viewed by 633
Abstract
Entropy can signify different things. For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced, and it can be difficult to ascertain their respective importance and merits. Here, we consider entropy in an abstract [...] Read more.
Entropy can signify different things. For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced, and it can be difficult to ascertain their respective importance and merits. Here, we consider entropy in an abstract sense, as a functional on a probability space, and we review how being able to handle the trivial case of non-interacting systems, together with the subtle requirement of extensivity, allows for a systematic classification of the functional form. Full article
24 pages, 755 KiB  
Article
Exact Results for Non-Newtonian Transport Properties in Sheared Granular Suspensions: Inelastic Maxwell Models and BGK-Type Kinetic Model
by Rubén Gómez González and Vicente Garzó
Entropy 2024, 26(3), 265; https://doi.org/10.3390/e26030265 - 15 Mar 2024
Viewed by 652
Abstract
The Boltzmann kinetic equation for dilute granular suspensions under simple (or uniform) shear flow (USF) is considered to determine the non-Newtonian transport properties of the system. In contrast to previous attempts based on a coarse-grained description, our suspension model accounts for the real [...] Read more.
The Boltzmann kinetic equation for dilute granular suspensions under simple (or uniform) shear flow (USF) is considered to determine the non-Newtonian transport properties of the system. In contrast to previous attempts based on a coarse-grained description, our suspension model accounts for the real collisions between grains and particles of the surrounding molecular gas. The latter is modeled as a bath (or thermostat) of elastic hard spheres at a given temperature. Two independent but complementary approaches are followed to reach exact expressions for the rheological properties. First, the Boltzmann equation for the so-called inelastic Maxwell models (IMM) is considered. The fact that the collision rate of IMM is independent of the relative velocity of the colliding spheres allows us to exactly compute the collisional moments of the Boltzmann operator without the knowledge of the distribution function. Thanks to this property, the transport properties of the sheared granular suspension can be exactly determined. As a second approach, a Bhatnagar–Gross–Krook (BGK)-type kinetic model adapted to granular suspensions is solved to compute the velocity moments and the velocity distribution function of the system. The theoretical results (which are given in terms of the coefficient of restitution, the reduced shear rate, the reduced background temperature, and the diameter and mass ratios) show, in general, a good agreement with the approximate analytical results derived for inelastic hard spheres (IHS) by means of Grad’s moment method and with computer simulations performed in the Brownian limiting case (m/mg, where mg and m are the masses of the particles of the molecular and granular gases, respectively). In addition, as expected, the IMM and BGK results show that the temperature and non-Newtonian viscosity exhibit an S shape in a plane of stress–strain rate (discontinuous shear thickening, DST). The DST effect becomes more pronounced as the mass ratio m/mg increases. Full article
(This article belongs to the Special Issue 180th Anniversary of Ludwig Boltzmann)
Show Figures

Figure 1

18 pages, 10036 KiB  
Article
Exploration of Resonant Modes for Circular and Polygonal Chladni Plates
by Amira Val Baker, Mate Csanad, Nicolas Fellas, Nour Atassi, Ia Mgvdliashvili and Paul Oomen
Entropy 2024, 26(3), 264; https://doi.org/10.3390/e26030264 - 15 Mar 2024
Viewed by 1343
Abstract
In general, sound waves propagate radially outwards from a point source. These waves will continue in the same direction, decreasing in intensity, unless a boundary condition is met. To arrive at a universal understanding of the relation between frequency and wave propagation within [...] Read more.
In general, sound waves propagate radially outwards from a point source. These waves will continue in the same direction, decreasing in intensity, unless a boundary condition is met. To arrive at a universal understanding of the relation between frequency and wave propagation within spatial boundaries, we explore the maximum entropy states that are realized as resonant modes. For both circular and polygonal Chladni plates, a model is presented that successfully recreates the nodal line patterns to a first approximation. We discuss the benefits of such a model and the future work necessary to develop the model to its full predictive ability. Full article
(This article belongs to the Section Signal and Data Analysis)
Show Figures

Figure 1

20 pages, 1465 KiB  
Article
A Numerical Study of Quantum Entropy and Information in the Wigner–Fokker–Planck Equation for Open Quantum Systems
by Arash Edrisi, Hamza Patwa and Jose A. Morales Escalante
Entropy 2024, 26(3), 263; https://doi.org/10.3390/e26030263 - 14 Mar 2024
Cited by 1 | Viewed by 710
Abstract
Kinetic theory provides modeling of open quantum systems subject to Markovian noise via the Wigner–Fokker–Planck equation, which is an alternate of the Lindblad master equation setting, having the advantage of great physical intuition as it is the quantum equivalent of the classical phase [...] Read more.
Kinetic theory provides modeling of open quantum systems subject to Markovian noise via the Wigner–Fokker–Planck equation, which is an alternate of the Lindblad master equation setting, having the advantage of great physical intuition as it is the quantum equivalent of the classical phase space description. We perform a numerical inspection of the Wehrl entropy for the benchmark problem of a harmonic potential, since the existence of a steady state and its analytical formula have been proven theoretically in this case. When there is friction in the noise terms, no theoretical results on the monotonicity of absolute entropy are available. We provide numerical results of the time evolution of the entropy in the case with friction using a stochastic (Euler–Maruyama-based Monte Carlo) numerical solver. For all the chosen initial conditions studied (all of them Gaussian states), up to the inherent numerical error of the method, one cannot disregard the possibility of monotonic behavior even in the case under study, where the noise includes friction terms. Full article
(This article belongs to the Special Issue 180th Anniversary of Ludwig Boltzmann)
Show Figures

Figure 1

22 pages, 537 KiB  
Article
CNN-HT: A Two-Stage Algorithm Selection Framework
by Siyi Xu, Wenwen Liu, Chengpei Wu and Junli Li
Entropy 2024, 26(3), 262; https://doi.org/10.3390/e26030262 - 14 Mar 2024
Viewed by 690
Abstract
The No Free Lunch Theorem tells us that no algorithm can beat other algorithms on all types of problems. The algorithm selection structure is proposed to select the most suitable algorithm from a set of algorithms for an unknown optimization problem. This paper [...] Read more.
The No Free Lunch Theorem tells us that no algorithm can beat other algorithms on all types of problems. The algorithm selection structure is proposed to select the most suitable algorithm from a set of algorithms for an unknown optimization problem. This paper introduces an innovative algorithm selection approach called the CNN-HT, which is a two-stage algorithm selection framework. In the first stage, a Convolutional Neural Network (CNN) is employed to classify problems. In the second stage, the Hypothesis Testing (HT) technique is used to suggest the best-performing algorithm based on the statistical analysis of the performance metric of algorithms that address various problem categories. The two-stage approach can adapt to different algorithm combinations without the need to retrain the entire model, and modifications can be made in the second stage only, which is an improvement of one-stage approaches. To provide a more general structure for the classification model, we adopt Exploratory Landscape Analysis (ELA) features of the problem as input and utilize feature selection techniques to reduce the redundant ones. In problem classification, the average accuracy of classifying problems using CNN is 96%, which demonstrates the advantages of CNN compared to Random Forest and Support Vector Machines. After feature selection, the accuracy increases to 98.8%, further improving the classification performance while reducing the computational cost. This demonstrates the effectiveness of the first stage of the CNN-HT method, which provides a basis for algorithm selection. In the experiments, CNN-HT shows the advantages of the second stage algorithm as well as good performance with better average rankings in different algorithm combinations compared to the individual algorithms and another algorithm combination approach. Full article
(This article belongs to the Special Issue Swarm Intelligence Optimization: Algorithms and Applications)
Show Figures

Figure 1

12 pages, 319 KiB  
Article
Magnetic Black Hole Thermodynamics in an Extended Phase Space with Nonlinear Electrodynamics
by Sergey Il’ich Kruglov
Entropy 2024, 26(3), 261; https://doi.org/10.3390/e26030261 - 14 Mar 2024
Viewed by 609
Abstract
We study Einstein’s gravity coupled to nonlinear electrodynamics with two parameters in anti-de Sitter spacetime. Magnetically charged black holes in an extended phase space are investigated. We obtain the mass and metric functions and the asymptotic and corrections to the Reissner–Nordström metric function [...] Read more.
We study Einstein’s gravity coupled to nonlinear electrodynamics with two parameters in anti-de Sitter spacetime. Magnetically charged black holes in an extended phase space are investigated. We obtain the mass and metric functions and the asymptotic and corrections to the Reissner–Nordström metric function when the cosmological constant vanishes. The first law of black hole thermodynamics in an extended phase space is formulated and the magnetic potential and the thermodynamic conjugate to the coupling are obtained. We prove the generalized Smarr relation. The heat capacity and the Gibbs free energy are computed and the phase transitions are studied. It is shown that the electric fields of charged objects at the origin and the electrostatic self-energy are finite within the nonlinear electrodynamics proposed. Full article
(This article belongs to the Special Issue Trends in the Second Law of Thermodynamics)
Show Figures

Figure 1

11 pages, 318 KiB  
Article
Restoring the Fluctuation–Dissipation Theorem in Kardar–Parisi–Zhang Universality Class through a New Emergent Fractal Dimension
by Márcio S. Gomes-Filho, Pablo de Castro, Danilo B. Liarte and Fernando A. Oliveira
Entropy 2024, 26(3), 260; https://doi.org/10.3390/e26030260 - 14 Mar 2024
Viewed by 586
Abstract
The Kardar–Parisi–Zhang (KPZ) equation describes a wide range of growth-like phenomena, with applications in physics, chemistry and biology. There are three central questions in the study of KPZ growth: the determination of height probability distributions; the search for ever more precise universal growth [...] Read more.
The Kardar–Parisi–Zhang (KPZ) equation describes a wide range of growth-like phenomena, with applications in physics, chemistry and biology. There are three central questions in the study of KPZ growth: the determination of height probability distributions; the search for ever more precise universal growth exponents; and the apparent absence of a fluctuation–dissipation theorem (FDT) for spatial dimension d>1. Notably, these questions were answered exactly only for 1+1 dimensions. In this work, we propose a new FDT valid for the KPZ problem in d+1 dimensions. This is achieved by rearranging terms and identifying a new correlated noise which we argue to be characterized by a fractal dimension dn. We present relations between the KPZ exponents and two emergent fractal dimensions, namely df, of the rough interface, and dn. Also, we simulate KPZ growth to obtain values for transient versions of the roughness exponent α, the surface fractal dimension df and, through our relations, the noise fractal dimension dn. Our results indicate that KPZ may have at least two fractal dimensions and that, within this proposal, an FDT is restored. Finally, we provide new insights into the old question about the upper critical dimension of the KPZ universality class. Full article
Show Figures

Figure 1

16 pages, 1798 KiB  
Article
Differential Entropy-Based Fault-Detection Mechanism for Power-Constrained Networked Control Systems
by Alejandro J. Rojas
Entropy 2024, 26(3), 259; https://doi.org/10.3390/e26030259 - 14 Mar 2024
Viewed by 586
Abstract
In this work, we consider the design of power-constrained networked control systems (NCSs) and a differential entropy-based fault-detection mechanism. For the NCS design of the control loop, we consider faults in the plant gain and unstable plant pole locations, either due to natural [...] Read more.
In this work, we consider the design of power-constrained networked control systems (NCSs) and a differential entropy-based fault-detection mechanism. For the NCS design of the control loop, we consider faults in the plant gain and unstable plant pole locations, either due to natural causes or malicious intent. Since the power-constrained approach utilized in the NCS design is a stationary approach, we then discuss the finite-time approximation of the power constraints for the relevant control loop signals. The network under study is formed by two additive white Gaussian noise (AWGN) channels located on the direct and feedback paths of the closed control loop. The finite-time approximation of the controller output signal allows us to estimate its differential entropy, which is used in our proposed fault-detection mechanism. After fault detection, we propose a fault-identification mechanism that is capable of correctly discriminating faults. Finally, we discuss the extension of the contributions developed here to future research directions, such as fault recovery and control resilience. Full article
Show Figures

Figure 1

16 pages, 3876 KiB  
Article
Three-Dimensional Reconstruction Pre-Training as a Prior to Improve Robustness to Adversarial Attacks and Spurious Correlation
by Yutaro Yamada, Fred Weiying Zhang, Yuval Kluger and Ilker Yildirim
Entropy 2024, 26(3), 258; https://doi.org/10.3390/e26030258 - 14 Mar 2024
Viewed by 633
Abstract
Ensuring robustness of image classifiers against adversarial attacks and spurious correlation has been challenging. One of the most effective methods for adversarial robustness is a type of data augmentation that uses adversarial examples during training. Here, inspired by computational models of human vision, [...] Read more.
Ensuring robustness of image classifiers against adversarial attacks and spurious correlation has been challenging. One of the most effective methods for adversarial robustness is a type of data augmentation that uses adversarial examples during training. Here, inspired by computational models of human vision, we explore a synthesis of this approach by leveraging a structured prior over image formation: the 3D geometry of objects and how it projects to images. We combine adversarial training with a weight initialization that implicitly encodes such a prior about 3D objects via 3D reconstruction pre-training. We evaluate our approach using two different datasets and compare it to alternative pre-training protocols that do not encode a prior about 3D shape. To systematically explore the effect of 3D pre-training, we introduce a novel dataset called Geon3D, which consists of simple shapes that nevertheless capture variation in multiple distinct dimensions of geometry. We find that while 3D reconstruction pre-training does not improve robustness for the simplest dataset setting, we consider (Geon3D on a clean background) that it improves upon adversarial training in more realistic (Geon3D with textured background and ShapeNet) conditions. We also find that 3D pre-training coupled with adversarial training improves the robustness to spurious correlations between shape and background textures. Furthermore, we show that the benefit of using 3D-based pre-training outperforms 2D-based pre-training on ShapeNet. We hope that these results encourage further investigation of the benefits of structured, 3D-based models of vision for adversarial robustness. Full article
(This article belongs to the Special Issue Probabilistic Models in Machine and Human Learning)
Show Figures

Figure 1

14 pages, 737 KiB  
Article
Analysis of Quantum Steering Measures
by Lucas Maquedano and Ana C. S. Costa
Entropy 2024, 26(3), 257; https://doi.org/10.3390/e26030257 - 14 Mar 2024
Viewed by 676
Abstract
The effect of quantum steering describes a possible action at a distance via local measurements. In the last few years, several criteria have been proposed to detect this type of correlation in quantum systems. However, there are few approaches presented in order to [...] Read more.
The effect of quantum steering describes a possible action at a distance via local measurements. In the last few years, several criteria have been proposed to detect this type of correlation in quantum systems. However, there are few approaches presented in order to measure the degree of steerability of a given system. In this work, we are interested in investigating possible ways to quantify quantum steering, where we based our analysis on different criteria presented in the literature. Full article
(This article belongs to the Special Issue Quantum Correlations, Contextuality, and Quantum Nonlocality)
Show Figures

Figure 1

15 pages, 2895 KiB  
Article
Patterns in Temporal Networks with Higher-Order Egocentric Structures
by Beatriz Arregui-García, Antonio Longa, Quintino Francesco Lotito, Sandro Meloni and Giulia Cencetti
Entropy 2024, 26(3), 256; https://doi.org/10.3390/e26030256 - 13 Mar 2024
Cited by 1 | Viewed by 691
Abstract
The analysis of complex and time-evolving interactions, such as those within social dynamics, represents a current challenge in the science of complex systems. Temporal networks stand as a suitable tool for schematizing such systems, encoding all the interactions appearing between pairs of individuals [...] Read more.
The analysis of complex and time-evolving interactions, such as those within social dynamics, represents a current challenge in the science of complex systems. Temporal networks stand as a suitable tool for schematizing such systems, encoding all the interactions appearing between pairs of individuals in discrete time. Over the years, network science has developed many measures to analyze and compare temporal networks. Some of them imply a decomposition of the network into small pieces of interactions; i.e., only involving a few nodes for a short time range. Along this line, a possible way to decompose a network is to assume an egocentric perspective; i.e., to consider for each node the time evolution of its neighborhood. This was proposed by Longa et al. by defining the “egocentric temporal neighborhood”, which has proven to be a useful tool for characterizing temporal networks relative to social interactions. However, this definition neglects group interactions (quite common in social domains), as they are always decomposed into pairwise connections. A more general framework that also allows considering larger interactions is represented by higher-order networks. Here, we generalize the description of social interactions to hypergraphs. Consequently, we generalize their decomposition into “hyper egocentric temporal neighborhoods”. This enables the analysis of social interactions, facilitating comparisons between different datasets or nodes within a dataset, while considering the intrinsic complexity presented by higher-order interactions. Even if we limit the order of interactions to the second order (triplets of nodes), our results reveal the importance of a higher-order representation.In fact, our analyses show that second-order structures are responsible for the majority of the variability at all scales: between datasets, amongst nodes, and over time. Full article
Show Figures

Figure 1

12 pages, 3364 KiB  
Article
Events as Elements of Physical Observation: Experimental Evidence
by J. Gerhard Müller
Entropy 2024, 26(3), 255; https://doi.org/10.3390/e26030255 - 13 Mar 2024
Viewed by 871
Abstract
It is argued that all physical knowledge ultimately stems from observation and that the simplest possible observation is that an event has happened at a certain space–time location X=x,t. Considering historic experiments, which have been groundbreaking [...] Read more.
It is argued that all physical knowledge ultimately stems from observation and that the simplest possible observation is that an event has happened at a certain space–time location X=x,t. Considering historic experiments, which have been groundbreaking in the evolution of our modern ideas of matter on the atomic, nuclear, and elementary particle scales, it is shown that such experiments produce as outputs streams of macroscopically observable events which accumulate in the course of time into spatio-temporal patterns of events whose forms allow decisions to be taken concerning conceivable alternatives of explanation. Working towards elucidating the physical and informational characteristics of those elementary observations, we show that these represent hugely amplified images of the initiating micro-events and that the resulting macro-images have a cognitive value of 1 bit and a physical value of Wobs=Eobsτobsh. In this latter equation, Eobs stands for the energy spent in turning the initiating micro-events into macroscopically observable events, τobs for the lifetimes during which the generated events remain macroscopically observable, and h for Planck’s constant. The relative value Gobs=Wobs/h finally represents a measure of amplification that was gained in the observation process. Full article
Show Figures

Figure 1

23 pages, 36196 KiB  
Article
An n-Dimensional Chaotic Map with Application in Reversible Data Hiding for Medical Images
by Yuli Yang, Ruiyun Chang, Xiufang Feng, Peizhen Li, Yongle Chen and Hao Zhang
Entropy 2024, 26(3), 254; https://doi.org/10.3390/e26030254 - 13 Mar 2024
Viewed by 652
Abstract
The drawbacks of a one-dimensional chaotic map are its straightforward structure, abrupt intervals, and ease of signal prediction. Richer performance and a more complicated structure are required for multidimensional chaotic mapping. To address the shortcomings of current chaotic systems, an n-dimensional cosine-transform-based [...] Read more.
The drawbacks of a one-dimensional chaotic map are its straightforward structure, abrupt intervals, and ease of signal prediction. Richer performance and a more complicated structure are required for multidimensional chaotic mapping. To address the shortcomings of current chaotic systems, an n-dimensional cosine-transform-based chaotic system (nD-CTBCS) with a chaotic coupling model is suggested in this study. To create chaotic maps of any desired dimension, nD-CTBCS can take advantage of already-existing 1D chaotic maps as seed chaotic maps. Three two-dimensional chaotic maps are provided as examples to illustrate the impact. The findings of the evaluation and experiments demonstrate that the newly created chaotic maps function better, have broader chaotic intervals, and display hyperchaotic behavior. To further demonstrate the practicability of nD-CTBCS, a reversible data hiding scheme is proposed for the secure communication of medical images. The experimental results show that the proposed method has higher security than the existing methods. Full article
Show Figures

Figure 1

15 pages, 681 KiB  
Article
Intra-Beam Interference Mitigation for the Downlink Transmission of the RIS-Assisted Hybrid Millimeter Wave System
by Lou Zhao, Yuliang Zhang, Minjie Zhang and Chunshan Liu
Entropy 2024, 26(3), 253; https://doi.org/10.3390/e26030253 - 13 Mar 2024
Viewed by 687
Abstract
Millimeter-wave (mmWave) communication systems leverage the directional beamforming capabilities of antenna arrays equipped at the base stations (BS) to counteract the inherent high propagation path loss characteristic of mmWave channels. In downlink mmWave transmissions, i.e., from the BS to users, distinguishing users within [...] Read more.
Millimeter-wave (mmWave) communication systems leverage the directional beamforming capabilities of antenna arrays equipped at the base stations (BS) to counteract the inherent high propagation path loss characteristic of mmWave channels. In downlink mmWave transmissions, i.e., from the BS to users, distinguishing users within the same beam direction poses a significant challenge. Additionally, digital baseband precoding techniques are limited in their ability to mitigate inter-user interference within identical beam directions, representing a fundamental constraint in mmWave downlink transmissions. This study introduces an innovative analog beamforming-based interference mitigation strategy for downlink transmissions in reconfigurable intelligent surface (RIS)-assisted hybrid analog–digital (HAD) mmWave systems. This is achieved through the joint design of analog beamformers and the corresponding coefficients at both the RIS and the BS. We first present derived closed-form approximation expressions for the achievable rate performance in the proposed scenario and establish a stringent upper bound on this performance in a large number of RIS elements regimes. The exclusive use of analog beamforming in the downlink phase allows our proposed transmission algorithm to function efficiently when equipped with low-resolution analog-to-digital/digital-to-analog converters (A/Ds) at the BS. The energy efficiency of the downlink transmission is evaluated through the deployment of six-bit A/Ds and six-bit pulse-amplitude modulation (PAM) signals across varying numbers of activated RIS elements. Numerical simulation results validate the effectiveness of our proposed algorithms in comparison to various benchmark schemes. Full article
(This article belongs to the Section Signal and Data Analysis)
Show Figures

Figure 1

28 pages, 570 KiB  
Review
To Compress or Not to Compress—Self-Supervised Learning and Information Theory: A Review
by Ravid Shwartz Ziv and Yann LeCun
Entropy 2024, 26(3), 252; https://doi.org/10.3390/e26030252 - 12 Mar 2024
Cited by 18 | Viewed by 1746
Abstract
Deep neural networks excel in supervised learning tasks but are constrained by the need for extensive labeled data. Self-supervised learning emerges as a promising alternative, allowing models to learn without explicit labels. Information theory has shaped deep neural networks, particularly the information bottleneck [...] Read more.
Deep neural networks excel in supervised learning tasks but are constrained by the need for extensive labeled data. Self-supervised learning emerges as a promising alternative, allowing models to learn without explicit labels. Information theory has shaped deep neural networks, particularly the information bottleneck principle. This principle optimizes the trade-off between compression and preserving relevant information, providing a foundation for efficient network design in supervised contexts. However, its precise role and adaptation in self-supervised learning remain unclear. In this work, we scrutinize various self-supervised learning approaches from an information-theoretic perspective, introducing a unified framework that encapsulates the self-supervised information-theoretic learning problem. This framework includes multiple encoders and decoders, suggesting that all existing work on self-supervised learning can be seen as specific instances. We aim to unify these approaches to understand their underlying principles better and address the main challenge: many works present different frameworks with differing theories that may seem contradictory. By weaving existing research into a cohesive narrative, we delve into contemporary self-supervised methodologies, spotlight potential research areas, and highlight inherent challenges. Moreover, we discuss how to estimate information-theoretic quantities and their associated empirical problems. Overall, this paper provides a comprehensive review of the intersection of information theory, self-supervised learning, and deep neural networks, aiming for a better understanding through our proposed unified approach. Full article
Show Figures

Figure 1

17 pages, 8787 KiB  
Article
Multipole Approach to the Dynamical Casimir Effect with Finite-Size Scatterers
by Lucas Alonso, Guilherme C. Matos, François Impens, Paulo A. Maia Neto and Reinaldo de Melo e Souza
Entropy 2024, 26(3), 251; https://doi.org/10.3390/e26030251 - 12 Mar 2024
Viewed by 700
Abstract
A mirror subjected to a fast mechanical oscillation emits photons out of the quantum vacuum—a phenomenon known as the dynamical Casimir effect (DCE). The mirror is usually treated as an infinite metallic surface. Here, we show that, in realistic experimental conditions (mirror size [...] Read more.
A mirror subjected to a fast mechanical oscillation emits photons out of the quantum vacuum—a phenomenon known as the dynamical Casimir effect (DCE). The mirror is usually treated as an infinite metallic surface. Here, we show that, in realistic experimental conditions (mirror size and oscillation frequency), this assumption is inadequate and drastically overestimates the DCE radiation. Taking the opposite limit, we use instead the dipolar approximation to obtain a simpler and more realistic treatment of DCE for macroscopic bodies. Our approach is inspired by a microscopic theory of DCE, which is extended to the macroscopic realm by a suitable effective Hamiltonian description of moving anisotropic scatterers. We illustrate the benefits of our approach by considering the DCE from macroscopic bodies of different geometries. Full article
(This article belongs to the Special Issue Quantum Nonstationary Systems)
Show Figures

Figure 1

33 pages, 506 KiB  
Article
Fundamental Limits of Coded Caching in Request-Robust D2D Communication Networks
by Wuqu Wang, Zhe Tao, Nan Liu and Wei Kang
Entropy 2024, 26(3), 250; https://doi.org/10.3390/e26030250 - 12 Mar 2024
Viewed by 661
Abstract
D2D coded caching, originally introduced by Ji, Caire, and Molisch, significantly improves communication efficiency by applying the multi-cast technology proposed by Maddah-Ali and Niesen to the D2D network. Most prior works on D2D coded caching are based on the assumption that all users [...] Read more.
D2D coded caching, originally introduced by Ji, Caire, and Molisch, significantly improves communication efficiency by applying the multi-cast technology proposed by Maddah-Ali and Niesen to the D2D network. Most prior works on D2D coded caching are based on the assumption that all users will request content at the beginning of the delivery phase. However, in practice, this is often not the case. Motivated by this consideration, this paper formulates a new problem called request-robust D2D coded caching. The considered problem includes K users and a content server with access to N files. Only r users, known as requesters, request a file each at the beginning of the delivery phase. The objective is to minimize the average and worst-case delivery rate, i.e., the average and worst-case number of broadcast bits from all users among all possible demands. For this novel D2D coded caching problem, we propose a scheme based on uncoded cache placement and exploiting common demands and one-shot delivery. We also propose information-theoretic converse results under the assumption of uncoded cache placement. Furthermore, we adapt the scheme proposed by Yapar et al. for uncoded cache placement and one-shot delivery to the request-robust D2D coded caching problem and prove that the performance of the adapted scheme is order optimal within a factor of two under uncoded cache placement and within a factor of four in general. Finally, through numerical evaluations, we show that the proposed scheme outperforms known D2D coded caching schemes applied to the request-robust scenario for most cache size ranges. Full article
(This article belongs to the Special Issue Information Theory and Network Coding II)
Show Figures

Figure 1

18 pages, 401 KiB  
Article
Constrained Reweighting of Distributions: An Optimal Transport Approach
by Abhisek Chakraborty, Anirban Bhattacharya and Debdeep Pati
Entropy 2024, 26(3), 249; https://doi.org/10.3390/e26030249 - 11 Mar 2024
Viewed by 639
Abstract
We commonly encounter the problem of identifying an optimally weight-adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the moments, tail behavior, shapes, number of modes, etc., of the [...] Read more.
We commonly encounter the problem of identifying an optimally weight-adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the moments, tail behavior, shapes, number of modes, etc., of the resulting weight-adjusted empirical distribution. In this article, we substantially enhance the flexibility of such a methodology by introducing a nonparametrically imbued distributional constraint on the weights and developing a general framework leveraging the maximum entropy principle and tools from optimal transport. The key idea is to ensure that the maximum entropy weight-adjusted empirical distribution of the observed data is close to a pre-specified probability distribution in terms of the optimal transport metric, while allowing for subtle departures. The proposed scheme for the re-weighting of observations subject to constraints is reminiscent of the empirical likelihood and related ideas, but offers greater flexibility in applications where parametric distribution-guided constraints arise naturally. The versatility of the proposed framework is demonstrated in the context of three disparate applications where data re-weighting is warranted to satisfy side constraints on the optimization problem at the heart of the statistical task—namely, portfolio allocation, semi-parametric inference for complex surveys, and ensuring algorithmic fairness in machine learning algorithms. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
Show Figures

Figure 1

15 pages, 1251 KiB  
Article
Network Higher-Order Structure Dismantling
by Peng Peng, Tianlong Fan and Linyuan Lü
Entropy 2024, 26(3), 248; https://doi.org/10.3390/e26030248 - 11 Mar 2024
Viewed by 670
Abstract
Diverse higher-order structures, foundational for supporting a network’s “meta-functions”, play a vital role in structure, functionality, and the emergence of complex dynamics. Nevertheless, the problem of dismantling them has been consistently overlooked. In this paper, we introduce the concept of dismantling higher-order structures, [...] Read more.
Diverse higher-order structures, foundational for supporting a network’s “meta-functions”, play a vital role in structure, functionality, and the emergence of complex dynamics. Nevertheless, the problem of dismantling them has been consistently overlooked. In this paper, we introduce the concept of dismantling higher-order structures, with the objective of disrupting not only network connectivity but also eradicating all higher-order structures in each branch, thereby ensuring thorough functional paralysis. Given the diversity and unknown specifics of higher-order structures, identifying and targeting them individually is not practical or even feasible. Fortunately, their close association with k-cores arises from their internal high connectivity. Thus, we transform higher-order structure measurement into measurements on k-cores with corresponding orders. Furthermore, we propose the Belief Propagation-guided Higher-order Dismantling (BPHD) algorithm, minimizing dismantling costs while achieving maximal disruption to connectivity and higher-order structures, ultimately converting the network into a forest. BPHD exhibits the explosive vulnerability of network higher-order structures, counterintuitively showcasing decreasing dismantling costs with increasing structural complexity. Our findings offer a novel approach for dismantling malignant networks, emphasizing the substantial challenges inherent in safeguarding against such malicious attacks. Full article
(This article belongs to the Topic Complex Systems and Network Science)
Show Figures

Figure 1

1 pages, 381 KiB  
Correction
Correction: Zhou et al. Optimal Flow Distribution of Military Supply Transportation Based on Network Analysis and Entropy Measurement. Entropy 2018, 20, 446
by Wei Zhou, Jin Chen and Bingqing Ding
Entropy 2024, 26(3), 247; https://doi.org/10.3390/e26030247 - 11 Mar 2024
Viewed by 516
Abstract
In the original publication [...] Full article
Show Figures

Figure 5

10 pages, 325 KiB  
Article
Analysis of Self-Gravitating Fluid Instabilities from the Post-Newtonian Boltzmann Equation
by Gilberto M. Kremer
Entropy 2024, 26(3), 246; https://doi.org/10.3390/e26030246 - 10 Mar 2024
Viewed by 675
Abstract
Self-gravitating fluid instabilities are analysed within the framework of a post-Newtonian Boltzmann equation coupled with the Poisson equations for the gravitational potentials of the post-Newtonian theory. The Poisson equations are determined from the knowledge of the energy–momentum tensor calculated from a post-Newtonian Maxwell–Jüttner [...] Read more.
Self-gravitating fluid instabilities are analysed within the framework of a post-Newtonian Boltzmann equation coupled with the Poisson equations for the gravitational potentials of the post-Newtonian theory. The Poisson equations are determined from the knowledge of the energy–momentum tensor calculated from a post-Newtonian Maxwell–Jüttner distribution function. The one-particle distribution function and the gravitational potentials are perturbed from their background states, and the perturbations are represented by plane waves characterised by a wave number vector and time-dependent small amplitudes. The time-dependent amplitude of the one-particle distribution function is supposed to be a linear combination of the summational invariants of the post-Newtonian kinetic theory. From the coupled system of differential equations for the time-dependent amplitudes of the one-particle distribution function and gravitational potentials, an evolution equation for the mass density contrast is obtained. It is shown that for perturbation wavelengths smaller than the Jeans wavelength, the mass density contrast propagates as harmonic waves in time. For perturbation wavelengths greater than the Jeans wavelength, the mass density contrast grows in time, and the instability growth in the post-Newtonian theory is more accentuated than the one of the Newtonian theory. Full article
(This article belongs to the Special Issue Statistical Mechanics of Self-Gravitating Systems)
Show Figures

Figure 1

Previous Issue
Next Issue
Back to TopTop