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Entropy
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Entropy-based Methods in In and Out of Equilibrium Systems
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Entropy-based Methods in In and Out of Equilibrium Systems

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

Deadline for manuscript submissions: closed (31 December 2021) | Viewed by 13569

Special Issue Editor

Dr. Johan Anderson

E-Mail Website
Guest Editor
Department of Space, Earth and Environment, Chalmers University of Technology, SE-412 96 Göteborg, Sweden
Interests: anomalous diffusion; Tsallis entropy; nonlocal theory; Lévy noise; fractional Fokker–Plank equation
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

One of the major goals of statistical mechanics is the understanding of the time evolution of in and out of equilibrium systems. Many different approaches have been used; however, entropy-based methodologies are currently very common for analysis. Among the possible options is to work with the different metrics for the thermodynamic length and the information length, which is a generalization of the thermodynamic length to non-equilibrium systems. In particular, information length is computed as a distance in statistical space for time-evolving non-equilibrium systems and can possibly be used to identify the occurrence of coherent structures or rare events with large amplitudes. Other popular statistical measures such as “relative entropy” and “Jensen divergence” also concern comparing two PDFs (e.g., at two different times). This Special Issue aims to present current state-of-the-art modeling efforts that advance the understanding of entropy-based methods in in and out of equilibrium systems, e.g., dynamical systems, fluids, and plasmas and other fields. These are areas of particular interest, since there is strong evidence from laboratory experiments, observations, and computational studies that coherent structures can cause intermittent transport, significantly changing the dynamics. The Guest Editor is open to considering any paper relevant to the subject matter of the Special Issue.

Dr. Johan Anderson
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

  • turbulence
  • anomalous diffusion
  • Tsallis entropy
  • nonlocal theory
  • Lévy noise
  • fractional Fokker–Plank equation
  • fractional calculus/models
  • generalized statistical mechanics
  • q-Entropy/Tsallis entropy
  • intermittency
  • coherent structure
  • multiscale analysis
  • self-organization

Published Papers (7 papers)

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Research

23 pages, 566 KiB  
Article
Localization, Disorder, and Entropy in a Coarse-Grained Model of the Amorphous Solid
by Premkumar Leishangthem, Faizyab Ahmad and Shankar P. Das
Entropy 2021, 23(9), 1171; https://doi.org/10.3390/e23091171 - 06 Sep 2021
Cited by 1 | Viewed by 1586
Abstract
We study the role of disorder in producing the metastable states in which the extent of mass localization is intermediate between that of a liquid and a crystal with long-range order. We estimate the corresponding entropy with the coarse-grained description of a many-particle [...] Read more.
We study the role of disorder in producing the metastable states in which the extent of mass localization is intermediate between that of a liquid and a crystal with long-range order. We estimate the corresponding entropy with the coarse-grained description of a many-particle system used in the classical density functional model. We demonstrate that intermediate localization of the particles results in a change of the entropy from what is obtained from a microscopic approach using for sharply localized vibrational modes following a Debye distribution. An additional contribution is included in the density of vibrational states g(ω) to account for this excess entropy. A corresponding peak in g(ω)/ω2 vs. frequency ω matches the characteristic boson peak seen in amorphous solids. In the present work, we also compare the shear modulus for the inhomogeneous solid having localized density profiles with the corresponding elastic response for the uniform liquid in the limit of high frequencies. Full article
(This article belongs to the Special Issue Entropy-based Methods in In and Out of Equilibrium Systems)
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17 pages, 4344 KiB  
Article
A Theoretical Perspective of the Photochemical Potential in the Spectral Performance of Photovoltaic Cells
by Agustin Pérez-Madrid and Ivan Santamaría-Holek
Entropy 2021, 23(5), 579; https://doi.org/10.3390/e23050579 - 08 May 2021
Viewed by 1398
Abstract
We present a novel theoretical approach to the problem of light energy conversion in thermostated semiconductor junctions. Using the classical model of a two-level atom, we deduced formulas for the spectral response and the quantum efficiency in terms of the input photons’ non-zero [...] Read more.
We present a novel theoretical approach to the problem of light energy conversion in thermostated semiconductor junctions. Using the classical model of a two-level atom, we deduced formulas for the spectral response and the quantum efficiency in terms of the input photons’ non-zero chemical potential. We also calculated the spectral entropy production and the global efficiency parameter in the thermodynamic limit. The heat transferred to the thermostat results in a dissipative loss that appreciably controls the spectral quantities’ behavior and, therefore, the cell’s performance. The application of the obtained formulas to data extracted from photovoltaic cells enabled us to accurately interpolate experimental data for the spectral response and the quantum efficiency of cells based on Si-, GaAs, and CdTe, among others. Full article
(This article belongs to the Special Issue Entropy-based Methods in In and Out of Equilibrium Systems)
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15 pages, 269 KiB  
Article
Sustainable Performance Evaluation: Evidence from Listed Chinese Mining Corporations
by Yuan Ma, Jingzhi Men, Mingyu Li and Xiaoyan Li
Entropy 2021, 23(3), 349; https://doi.org/10.3390/e23030349 - 15 Mar 2021
Cited by 2 | Viewed by 1831
Abstract
Rapid industrial development has caused a series of environmental problems, which is not conducive to sustainable development of society as a whole. It is necessary to build a sustainable development evaluation system. Most of the existing literature has evaluated corporate sustainable performance from [...] Read more.
Rapid industrial development has caused a series of environmental problems, which is not conducive to sustainable development of society as a whole. It is necessary to build a sustainable development evaluation system. Most of the existing literature has evaluated corporate sustainable performance from the economy, environment and society on the basis of triple bottom lines. Considering the research gap and the practice need, an evaluation system is established from four dimensions, referred to as economy, society, environment and responsibility management, and 29 indicators are designed to measure these four dimensions. Twenty seven listed Chinese mining corporations are selected as research samples, and the entropy-weight-based Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method is applied to calculate indicators’ weights. Results show that the four dimensions of sustainable performance weights from high to low are society, environment, economy, and management process. Full article
(This article belongs to the Special Issue Entropy-based Methods in In and Out of Equilibrium Systems)
10 pages, 3839 KiB  
Article
Anisotropic Diffusion in Driven Convection Arrays
by Yunyun Li, Vyacheslav R. Misko, Fabio Marchesoni and Pulak K. Ghosh
Entropy 2021, 23(3), 343; https://doi.org/10.3390/e23030343 - 14 Mar 2021
Cited by 2 | Viewed by 1982
Abstract
We numerically investigate the transport of a Brownian colloidal particle in a square array of planar counter-rotating convection rolls at high Péclet numbers. We show that an external force produces huge excess peaks of the particle’s diffusion constant with a height that depends [...] Read more.
We numerically investigate the transport of a Brownian colloidal particle in a square array of planar counter-rotating convection rolls at high Péclet numbers. We show that an external force produces huge excess peaks of the particle’s diffusion constant with a height that depends on the force orientation and intensity. In sharp contrast, the particle’s mobility is isotropic and force independent. We relate such a nonlinear response of the system to the advection properties of the laminar flow in the suspension fluid. Full article
(This article belongs to the Special Issue Entropy-based Methods in In and Out of Equilibrium Systems)
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11 pages, 605 KiB  
Article
Negativity of the Casimir Self-Entropy in Spherical Geometries
by Yang Li, Kimball A. Milton, Prachi Parashar and Lujun Hong
Entropy 2021, 23(2), 214; https://doi.org/10.3390/e23020214 - 10 Feb 2021
Cited by 4 | Viewed by 1691
Abstract
It has been recognized for some time that, even for perfect conductors, the interaction Casimir entropy, due to quantum/thermal fluctuations, can be negative. This result was not considered problematic because it was thought that the self-entropies of the bodies would cancel this negative [...] Read more.
It has been recognized for some time that, even for perfect conductors, the interaction Casimir entropy, due to quantum/thermal fluctuations, can be negative. This result was not considered problematic because it was thought that the self-entropies of the bodies would cancel this negative interaction entropy, yielding a total entropy that was positive. In fact, this cancellation seems not to occur. The positive self-entropy of a perfectly conducting sphere does indeed just cancel the negative interaction entropy of a system consisting of a perfectly conducting sphere and plate, but a model with weaker coupling in general possesses a regime where negative self-entropy appears. The physical meaning of this surprising result remains obscure. In this paper, we re-examine these issues, using improved physical and mathematical techniques, partly based on the Abel–Plana formula, and present numerical results for arbitrary temperatures and couplings, which exhibit the same remarkable features. Full article
(This article belongs to the Special Issue Entropy-based Methods in In and Out of Equilibrium Systems)
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17 pages, 709 KiB  
Article
Structural Statistical Quantifiers and Thermal Features of Quantum Systems
by Flavia Pennini, Angelo Plastino, Angel Ricardo Plastino and Alberto Hernando
Entropy 2021, 23(1), 19; https://doi.org/10.3390/e23010019 - 25 Dec 2020
Cited by 2 | Viewed by 1776
Abstract
This paper deals primarily with relatively novel thermal quantifiers called disequilibrium and statistical complexity, whose role is growing in different disciplines of physics and other sciences. These quantifiers are called L. Ruiz, Mancini, and Calvet (LMC) quantifiers, following the initials of the three [...] Read more.
This paper deals primarily with relatively novel thermal quantifiers called disequilibrium and statistical complexity, whose role is growing in different disciplines of physics and other sciences. These quantifiers are called L. Ruiz, Mancini, and Calvet (LMC) quantifiers, following the initials of the three authors who advanced them. We wish to establish information-theoretical bridges between LMC structural quantifiers and (1) Thermal Heisenberg uncertainties ΔxΔp (at temperature T); (2) A nuclear physics fermion model. Having achieved such purposes, we determine to what an extent our bridges can be extended to both the semi-classical and classical realms. In addition, we find a strict bound relating a special LMC structural quantifier to quantum uncertainties. Full article
(This article belongs to the Special Issue Entropy-based Methods in In and Out of Equilibrium Systems)
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17 pages, 2239 KiB  
Article
Hydrodynamic and Thermodynamic Nonequilibrium Effects around Shock Waves: Based on a Discrete Boltzmann Method
by Chuandong Lin, Xianli Su and Yudong Zhang
Entropy 2020, 22(12), 1397; https://doi.org/10.3390/e22121397 - 10 Dec 2020
Cited by 12 | Viewed by 2452
Abstract
A shock wave that is characterized by sharp physical gradients always draws the medium out of equilibrium. In this work, both hydrodynamic and thermodynamic nonequilibrium effects around the shock wave are investigated using a discrete Boltzmann model. Via Chapman–Enskog analysis, the local equilibrium [...] Read more.
A shock wave that is characterized by sharp physical gradients always draws the medium out of equilibrium. In this work, both hydrodynamic and thermodynamic nonequilibrium effects around the shock wave are investigated using a discrete Boltzmann model. Via Chapman–Enskog analysis, the local equilibrium and nonequilibrium velocity distribution functions in one-, two-, and three-dimensional velocity space are recovered across the shock wave. Besides, the absolute and relative deviation degrees are defined in order to describe the departure of the fluid system from the equilibrium state. The local and global nonequilibrium effects, nonorganized energy, and nonorganized energy flux are also investigated. Moreover, the impacts of the relaxation frequency, Mach number, thermal conductivity, viscosity, and the specific heat ratio on the nonequilibrium behaviours around shock waves are studied. This work is helpful for a deeper understanding of the fine structures of shock wave and nonequilibrium statistical mechanics. Full article
(This article belongs to the Special Issue Entropy-based Methods in In and Out of Equilibrium Systems)
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