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Entropy
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Entropy Measures and Applications in Astrophysics
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Entropy Measures and Applications in Astrophysics

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Astrophysics, Cosmology, and Black Holes".

Deadline for manuscript submissions: closed (31 August 2022) | Viewed by 14303

Special Issue Editor

Prof. Dr. Manfred P. Leubner

E-Mail Website
Guest Editor
University of Innsbruck, Austria
Interests: theoretical astrophysics; plasma physics; kinetic theory; nonextensive statistics; entropy measures; self-gravitating systems; astrophysical turbulence; dark matter

Special Issue Information

Dear Colleagues,

Astrophysical structures are generally subject to spatial or temporal nonlocal interactions and correlations evolving in a non-Euclidean and multifractal spacetime that makes their behavior nonextensive. Inspired by the Renyi entropy measure, during the last three decades, a variety of nonextensive entropy concepts were developed, suitably extending the standard additivity of the classical Boltzmann–Gibbs extensive thermostatistics. The resulting power law distributions were associated with astrophysical observations and empirical space plasma kappa distributions were fundamentally linked to Tsallis statistics along with investigations of stationary states far from equilibrium or the analysis of fully developed turbulence based on nonextensive probability distribution functions. Remarkably, we have to add scale invariant power law distributions, relying on self-organized criticality as well as gravitationally bound stellar systems or dark matter density distributions in galaxies. Recently, nonextensive holographic dark energy models as well as attempts to understand modified Newtonian dynamics MOND within alternative entropy concepts were proposed.

This Special Issue aims to illuminate the power of nonextensive entropy paths for theoretical investigations and applications in view of nonlocal interactions in astrophysical structures with the goal of highlighting recent interdisciplinary developments, applications, and the universality of entropy measures.

In this Special Issue, submissions related but not limited to the following topics are welcome:

- Entropy measures favored in astrophysical environments, superstatistics

- Nonextensive power law distributions and applications, concept of temperature

- Long-range interactions, correlations, and memory; probability distribution functions in astrophysical turbulence; scaling properties and intermittency

- Nonextensivity of self-gravitating systems, theoretical and observational determination and interpretation of the entropic index

- Self similarity, fractal structures in astrophysics and nonextensive statistics

- Stationary states far from equilibrium, relaxation and cooperative dynamics in complex out-of-equilibrium systems

- Nonextensive dark matter and dark energy models and approaches to MOND

Prof. Dr. Manfred P. Leubner
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • astrophysics
  • thermostatistics
  • entropy measures
  • nonextensivity
  • complexity
  • self-gravity
  • dark matter

Published Papers (6 papers)

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Research

5 pages, 251 KiB  
Article
Gamow Temperature in Tsallis and Kaniadakis Statistics
by Hooman Moradpour, Mohsen Javaherian, Ebrahim Namvar and Amir Hadi Ziaie
Entropy 2022, 24(6), 797; https://doi.org/10.3390/e24060797 - 08 Jun 2022
Cited by 5 | Viewed by 1250
Abstract
Relying on the quantum tunnelling concept and Maxwell–Boltzmann–Gibbs statistics, Gamow shows that the star-burning process happens at temperatures comparable to a critical value, called the Gamow temperature (T) and less than the prediction of the classical framework. In order to highlight [...] Read more.
Relying on the quantum tunnelling concept and Maxwell–Boltzmann–Gibbs statistics, Gamow shows that the star-burning process happens at temperatures comparable to a critical value, called the Gamow temperature (T) and less than the prediction of the classical framework. In order to highlight the role of the equipartition theorem in the Gamow argument, a thermal length scale is defined, and then the effects of non-extensivity on the Gamow temperature have been investigated by focusing on the Tsallis and Kaniadakis statistics. The results attest that while the Gamow temperature decreases in the framework of Kaniadakis statistics, it can be bigger or smaller than T when Tsallis statistics are employed. Full article
(This article belongs to the Special Issue Entropy Measures and Applications in Astrophysics)
37 pages, 1335 KiB  
Article
Intrinsic Entropy of Squeezed Quantum Fields and Nonequilibrium Quantum Dynamics of Cosmological Perturbations
by Jen-Tsung Hsiang and Bei-Lok Hu
Entropy 2021, 23(11), 1544; https://doi.org/10.3390/e23111544 - 20 Nov 2021
Cited by 8 | Viewed by 1724
Abstract
Density contrasts in the universe are governed by scalar cosmological perturbations which, when expressed in terms of gauge-invariant variables, contain a classical component from scalar metric perturbations and a quantum component from inflaton field fluctuations. It has long been known that the effect [...] Read more.
Density contrasts in the universe are governed by scalar cosmological perturbations which, when expressed in terms of gauge-invariant variables, contain a classical component from scalar metric perturbations and a quantum component from inflaton field fluctuations. It has long been known that the effect of cosmological expansion on a quantum field amounts to squeezing. Thus, the entropy of cosmological perturbations can be studied by treating them in the framework of squeezed quantum systems. Entropy of a free quantum field is a seemingly simple yet subtle issue. In this paper, different from previous treatments, we tackle this issue with a fully developed nonequilibrium quantum field theory formalism for such systems. We compute the covariance matrix elements of the parametric quantum field and solve for the evolution of the density matrix elements and the Wigner functions, and, from them, derive the von Neumann entropy. We then show explicitly why the entropy for the squeezed yet closed system is zero, but is proportional to the particle number produced upon coarse-graining out the correlation between the particle pairs. We also construct the bridge between our quantum field-theoretic results and those using the probability distribution of classical stochastic fields by earlier authors, preserving some important quantum properties, such as entanglement and coherence, of the quantum field. Full article
(This article belongs to the Special Issue Entropy Measures and Applications in Astrophysics)
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8 pages, 293 KiB  
Article
Parker’s Solar Wind Model for a Polytropic Gas
by Bhimsen Shivamoggi, David Rollins and Leos Pohl
Entropy 2021, 23(11), 1497; https://doi.org/10.3390/e23111497 - 12 Nov 2021
Cited by 3 | Viewed by 1707
Abstract
Parker’s hydrodynamic isothermal solar wind model is extended to apply for a more realistic polytropic gas flow that can be caused by a variable extended heating of the corona. A compatible theoretical formulation is given and detailed numerical and systematic asymptotic theoretical considerations [...] Read more.
Parker’s hydrodynamic isothermal solar wind model is extended to apply for a more realistic polytropic gas flow that can be caused by a variable extended heating of the corona. A compatible theoretical formulation is given and detailed numerical and systematic asymptotic theoretical considerations are presented. The polytropic conditions favor an enhanced conversion of thermal energy in the solar wind into kinetic energy of the outward flow and are hence shown to enhance the acceleration of the solar wind, thus indicating a quicker loss of the solar angular momentum. Full article
(This article belongs to the Special Issue Entropy Measures and Applications in Astrophysics)
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14 pages, 1415 KiB  
Article
Testing the Steady-State Fluctuation Relation in the Solar Photospheric Convection
by Giorgio Viavattene, Giuseppe Consolini, Luca Giovannelli, Francesco Berrilli, Dario Del Moro, Fabio Giannattasio, Valentina Penza and Daniele Calchetti
Entropy 2020, 22(7), 716; https://doi.org/10.3390/e22070716 - 28 Jun 2020
Cited by 5 | Viewed by 2929
Abstract
The turbulent thermal convection on the Sun is an example of an irreversible non-equilibrium phenomenon in a quasi-steady state characterized by a continuous entropy production rate. Here, the statistical features of a proxy of the local entropy production rate, in solar quiet regions [...] Read more.
The turbulent thermal convection on the Sun is an example of an irreversible non-equilibrium phenomenon in a quasi-steady state characterized by a continuous entropy production rate. Here, the statistical features of a proxy of the local entropy production rate, in solar quiet regions at different timescales, are investigated and compared with the symmetry conjecture of the steady-state fluctuation theorem by Gallavotti and Cohen. Our results show that solar turbulent convection satisfies the symmetries predicted by the fluctuation relation of the Gallavotti and Cohen theorem at a local level. Full article
(This article belongs to the Special Issue Entropy Measures and Applications in Astrophysics)
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15 pages, 766 KiB  
Article
Nonextensive Statistical Mechanics: Equivalence Between Dual Entropy and Dual Probabilities
by George Livadiotis
Entropy 2020, 22(6), 594; https://doi.org/10.3390/e22060594 - 26 May 2020
Cited by 1 | Viewed by 2656
Abstract
The concept of duality of probability distributions constitutes a fundamental “brick” in the solid framework of nonextensive statistical mechanics—the generalization of Boltzmann–Gibbs statistical mechanics under the consideration of the q-entropy. The probability duality is solving old-standing issues of the theory, e.g., it [...] Read more.
The concept of duality of probability distributions constitutes a fundamental “brick” in the solid framework of nonextensive statistical mechanics—the generalization of Boltzmann–Gibbs statistical mechanics under the consideration of the q-entropy. The probability duality is solving old-standing issues of the theory, e.g., it ascertains the additivity for the internal energy given the additivity in the energy of microstates. However, it is a rather complex part of the theory, and certainly, it cannot be trivially explained along the Gibb’s path of entropy maximization. Recently, it was shown that an alternative picture exists, considering a dual entropy, instead of a dual probability. In particular, the framework of nonextensive statistical mechanics can be equivalently developed using q- and 1/q- entropies. The canonical probability distribution coincides again with the known q-exponential distribution, but without the necessity of the duality of ordinary-escort probabilities. Furthermore, it is shown that the dual entropies, q-entropy and 1/q-entropy, as well as, the 1-entropy, are involved in an identity, useful in theoretical development and applications. Full article
(This article belongs to the Special Issue Entropy Measures and Applications in Astrophysics)
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15 pages, 2572 KiB  
Article
Statistical Uncertainties of Space Plasma Properties Described by Kappa Distributions
by Georgios Nicolaou and George Livadiotis
Entropy 2020, 22(5), 541; https://doi.org/10.3390/e22050541 - 13 May 2020
Cited by 7 | Viewed by 2733
Abstract
The velocities of space plasma particles often follow kappa distribution functions, which have characteristic high energy tails. The tails of these distributions are associated with low particle flux and, therefore, it is challenging to precisely resolve them in plasma measurements. On the [...] Read more.
The velocities of space plasma particles often follow kappa distribution functions, which have characteristic high energy tails. The tails of these distributions are associated with low particle flux and, therefore, it is challenging to precisely resolve them in plasma measurements. On the other hand, the accurate determination of kappa distribution functions within a broad range of energies is crucial for the understanding of physical mechanisms. Standard analyses of the plasma observations determine the plasma bulk parameters from the statistical moments of the underlined distribution. It is important, however, to also quantify the uncertainties of the derived plasma bulk parameters, which determine the confidence level of scientific conclusions. We investigate the determination of the plasma bulk parameters from observations by an ideal electrostatic analyzer. We derive simple formulas to estimate the statistical uncertainties of the calculated bulk parameters. We then use the forward modelling method to simulate plasma observations by a typical top-hat electrostatic analyzer. We analyze the simulated observations in order to derive the plasma bulk parameters and their uncertainties. Our simulations validate our simplified formulas. We further examine the statistical errors of the plasma bulk parameters for several shapes of the plasma velocity distribution function. Full article
(This article belongs to the Special Issue Entropy Measures and Applications in Astrophysics)
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