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Entropy
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Entropy and Non-Equilibrium Statistical Mechanics
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Entropy and Non-Equilibrium Statistical Mechanics

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Statistical Physics".

Deadline for manuscript submissions: closed (18 March 2020) | Viewed by 30116

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editors

Dr. Antonio M. Scarfone

E-Mail Website
Guest Editor
Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche (ISC-CNR), c/o DISAT, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy
Interests: nonextensive statistical mechanics; nonlinear Fokker–Planck equations; geometry information; nonlinear Schroedinger equation; quantum groups and quantum algebras; complex systems
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Sumiyoshi Abe

E-Mail Website
Guest Editor
1. Department of Physics, Huaqiao University, Xiamen 361021, China
2. Institute of Physics, Kazan Federal University, 420008 Kazan, Russia
3. Department of Natural and Mathematical Sciences, Turin Polytechnic University in Tashkent, Tashkent 100095, Uzbekistan
Interests: statistical mechanics; quantum entanglement and quantum information; complex systems
Dr. Róbert Kovács

E-Mail Website
Guest Editor
1. Department of Theoretical Physics, Wigner Research Center of Physics, Hungarian Academy of Science, Konkoly-Thege M. 29-33, 1121 Budapest, Hungary
2. Department of Energy Engineering, Faculty of Mechanical Engineering, Budapest University of Technology and Economics, 1111 Budapest, Hungary
Interests: continuum mechanics and thermodynamics; internal variables; kinetic theory; numerical and analytical solutions of partial differential equations
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Non-equilibrium statistical mechanics has a long history and diverse aspects. It has been a major research field in physics and will remain so in the future. Even regarding the concept of entropy, there exists a longstanding problem concerning its definition for a system in a state far from equilibrium.

The aim of this Special Issue is to offer the possibility to discuss and present up-to-date problems that may not be restricted to statistical mechanics. Theoretical and experimental papers are both accepted and unifying research works that address both of them are encouraged. As the entropy itself is the central element of non-equilibrium processes, papers discussing various formulations of the second law and consequences are also welcome.

In this Special Issue, recent progress in kinetic approaches to hydrodynamics, rational extended thermodynamics, entropy in a strongly non-equilibrium stationary state, and related topics will be reported. Review articles as well as the original research works will be presented.

Dr. Antonio M. Scarfone
Prof. Dr. Sumiyoshi Abe
Dr. Róbert Kovács
Guest Editors

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

  • non-equilibrium phenomena
  • kinetic theory
  • second law of thermodynamics
  • statistical distributions
  • stochastic processes

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Published Papers (8 papers)

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Editorial

Jump to: Research

2 pages, 149 KiB  
Editorial
Entropy and Non-Equilibrium Statistical Mechanics
by Róbert Kovács, Antonio M. Scarfone and Sumiyoshi Abe
Entropy 2020, 22(5), 507; https://doi.org/10.3390/e22050507 - 29 Apr 2020
Cited by 1 | Viewed by 2306
Abstract
The present Special Issue, ‘Entropy and Non-Equilibrium Statistical Mechanics’, consists of seven original research papers [...] Full article
(This article belongs to the Special Issue Entropy and Non-Equilibrium Statistical Mechanics)

Research

Jump to: Editorial

12 pages, 759 KiB  
Article
Classical Model of Quons
by Giorgio Kaniadakis and Antonio M. Scarfone
Entropy 2019, 21(9), 841; https://doi.org/10.3390/e21090841 - 27 Aug 2019
Cited by 2 | Viewed by 2402
Abstract
By using the kinetic interaction principle, the quons statistics in the framework of kinetic theory is introduced. This is done by properly generalizing the inclusion/exclusion principle of standard boson and fermion statistics within a nonlinear classical model. The related nonlinear Fokker-Planck equation is [...] Read more.
By using the kinetic interaction principle, the quons statistics in the framework of kinetic theory is introduced. This is done by properly generalizing the inclusion/exclusion principle of standard boson and fermion statistics within a nonlinear classical model. The related nonlinear Fokker-Planck equation is introduced and the corresponding steady distribution describing quons statistics of type I and type II is derived. Full article
(This article belongs to the Special Issue Entropy and Non-Equilibrium Statistical Mechanics)
13 pages, 823 KiB  
Article
Statistics of the Bifurcation in Quantum Measurement
by Karl-Erik Eriksson and Kristian Lindgren
Entropy 2019, 21(9), 834; https://doi.org/10.3390/e21090834 - 26 Aug 2019
Cited by 3 | Viewed by 3336
Abstract
We model quantum measurement of a two-level system μ . Previous obstacles for understanding the measurement process are removed by basing the analysis of the interaction between μ and the measurement device on quantum field theory. This formulation shows how inverse processes take [...] Read more.
We model quantum measurement of a two-level system μ . Previous obstacles for understanding the measurement process are removed by basing the analysis of the interaction between μ and the measurement device on quantum field theory. This formulation shows how inverse processes take part in the interaction and introduce a non-linearity, necessary for the bifurcation of quantum measurement. A statistical analysis of the ensemble of initial states of the measurement device shows how microscopic details can influence the transition to a final state. We find that initial states that are efficient in leading to a transition to a final state result in either of the expected eigenstates for μ , with ensemble averages that are identical to the probabilities of the Born rule. Thus, the proposed scheme serves as a candidate mechanism for the quantum measurement process. Full article
(This article belongs to the Special Issue Entropy and Non-Equilibrium Statistical Mechanics)
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13 pages, 597 KiB  
Article
On the Rarefied Gas Experiments
by Róbert Kovács
Entropy 2019, 21(7), 718; https://doi.org/10.3390/e21070718 - 23 Jul 2019
Cited by 9 | Viewed by 3557
Abstract
There are limits of validity of classical constitutive laws such as Fourier and Navier-Stokes equations. Phenomena beyond those limits have been experimentally found many decades ago. However, it is still not clear what theory would be appropriate to model different non-classical phenomena under [...] Read more.
There are limits of validity of classical constitutive laws such as Fourier and Navier-Stokes equations. Phenomena beyond those limits have been experimentally found many decades ago. However, it is still not clear what theory would be appropriate to model different non-classical phenomena under different conditions considering either the low-temperature or composite material structure. In this paper, a modeling problem of rarefied gases is addressed. The discussion covers the mass density dependence of material parameters, the scaling properties of different theories and aspects of how to model an experiment. In the following, two frameworks and their properties are presented. One of them is the kinetic theory based Rational Extended Thermodynamics; the other one is the non-equilibrium thermodynamics with internal variables and current multipliers. In order to compare these theories, an experiment on sound speed in rarefied gases at high frequencies, performed by Rhodes, is analyzed in detail. It is shown that the density dependence of material parameters could have a severe impact on modeling capabilities and influences the scaling properties. Full article
(This article belongs to the Special Issue Entropy and Non-Equilibrium Statistical Mechanics)
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18 pages, 282 KiB  
Communication
A Note on the Entropy Force in Kinetic Theory and Black Holes
by Rudolf A. Treumann and Wolfgang Baumjohann
Entropy 2019, 21(7), 716; https://doi.org/10.3390/e21070716 - 23 Jul 2019
Cited by 6 | Viewed by 4426
Abstract
The entropy force is the collective effect of inhomogeneity in disorder in a statistical many particle system. We demonstrate its presumable effect on one particular astrophysical object, the black hole. We then derive the kinetic equations of a large system of particles including [...] Read more.
The entropy force is the collective effect of inhomogeneity in disorder in a statistical many particle system. We demonstrate its presumable effect on one particular astrophysical object, the black hole. We then derive the kinetic equations of a large system of particles including the entropy force. It adds a collective therefore integral term to the Klimontovich equation for the evolution of the one-particle distribution function. Its integral character transforms the basic one particle kinetic equation into an integro-differential equation already on the elementary level, showing that not only the microscopic forces but the hole system reacts to its evolution of its probability distribution in a holistic way. It also causes a collisionless dissipative term which however is small in the inverse particle number and thus negligible. However it contributes an entropic collisional dissipation term. The latter is defined via the particle correlations but lacks any singularities and thus is large scale. It allows also for the derivation of a kinetic equation for the entropy density in phase space. This turns out to be of same structure as the equation for the phase space density. The entropy density determines itself holistically via the integral entropy force thus providing a self-controlled evolution of entropy in phase space. Full article
(This article belongs to the Special Issue Entropy and Non-Equilibrium Statistical Mechanics)
27 pages, 336 KiB  
Article
Dynamic Maximum Entropy Reduction
by Václav Klika, Michal Pavelka, Petr Vágner and Miroslav Grmela
Entropy 2019, 21(7), 715; https://doi.org/10.3390/e21070715 - 22 Jul 2019
Cited by 24 | Viewed by 5258
Abstract
Any physical system can be regarded on different levels of description varying by how detailed the description is. We propose a method called Dynamic MaxEnt (DynMaxEnt) that provides a passage from the more detailed evolution equations to equations for the less detailed state [...] Read more.
Any physical system can be regarded on different levels of description varying by how detailed the description is. We propose a method called Dynamic MaxEnt (DynMaxEnt) that provides a passage from the more detailed evolution equations to equations for the less detailed state variables. The method is based on explicit recognition of the state and conjugate variables, which can relax towards the respective quasi-equilibria in different ways. Detailed state variables are reduced using the usual principle of maximum entropy (MaxEnt), whereas relaxation of conjugate variables guarantees that the reduced equations are closed. Moreover, an infinite chain of consecutive DynMaxEnt approximations can be constructed. The method is demonstrated on a particle with friction, complex fluids (equipped with conformation and Reynolds stress tensors), hyperbolic heat conduction and magnetohydrodynamics. Full article
(This article belongs to the Special Issue Entropy and Non-Equilibrium Statistical Mechanics)
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8 pages, 308 KiB  
Article
A Fourth Order Entropy Stable Scheme for Hyperbolic Conservation Laws
by Xiaohan Cheng
Entropy 2019, 21(5), 508; https://doi.org/10.3390/e21050508 - 19 May 2019
Cited by 6 | Viewed by 4291
Abstract
This paper develops a fourth order entropy stable scheme to approximate the entropy solution of one-dimensional hyperbolic conservation laws. The scheme is constructed by employing a high order entropy conservative flux of order four in conjunction with a suitable numerical diffusion operator that [...] Read more.
This paper develops a fourth order entropy stable scheme to approximate the entropy solution of one-dimensional hyperbolic conservation laws. The scheme is constructed by employing a high order entropy conservative flux of order four in conjunction with a suitable numerical diffusion operator that based on a fourth order non-oscillatory reconstruction which satisfies the sign property. The constructed scheme possesses two features: (1) it achieves fourth order accuracy in the smooth area while keeping high resolution with sharp discontinuity transitions in the nonsmooth area; (2) it is entropy stable. Some typical numerical experiments are performed to illustrate the capability of the new entropy stable scheme. Full article
(This article belongs to the Special Issue Entropy and Non-Equilibrium Statistical Mechanics)
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7 pages, 225 KiB  
Article
Spin Isoenergetic Process and the Lindblad Equation
by Congjie Ou, Yuho Yokoi and Sumiyoshi Abe
Entropy 2019, 21(5), 503; https://doi.org/10.3390/e21050503 - 17 May 2019
Cited by 6 | Viewed by 3280
Abstract
A general comment is made on the existence of various baths in quantum thermodynamics, and a brief explanation is presented about the concept of weak invariants. Then, the isoenergetic process is studied for a spin in a magnetic field that slowly varies in [...] Read more.
A general comment is made on the existence of various baths in quantum thermodynamics, and a brief explanation is presented about the concept of weak invariants. Then, the isoenergetic process is studied for a spin in a magnetic field that slowly varies in time. In the Markovian approximation, the corresponding Lindbladian operators are constructed without recourse to detailed information about the coupling of the subsystem with the environment called the energy bath. The entropy production rate under the resulting Lindblad equation is shown to be positive. The leading-order expressions of the power output and work done along the isoenergetic process are obtained. Full article
(This article belongs to the Special Issue Entropy and Non-Equilibrium Statistical Mechanics)
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