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Entropy
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Applications of Statistical Thermodynamics
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Applications of Statistical Thermodynamics

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

Deadline for manuscript submissions: closed (18 March 2020) | Viewed by 18502

Special Issue Editor

Dr. Nobumitsu Shohoji

E-Mail Website
Guest Editor
Independent Researcher, 1649-038 Lisboa, Portugal
Interests: statistical thermodynamic analysis of non-stoichiometric interstitial compounds; synthesis of carbide, nitride and carbo-nitride (using concentrated solar beam as the heat source as well as using conventional electric furnace); formation and characterization of non-equilibrium solid phases

Special Issue Information

Dear Colleagues,

Statistical thermodynamics span the bridge between the visible macroscopic world and the invisible atomistic world to evaluate values of atomistic interaction parameters with unambiguous physical significance from measured values of state parameters, such as temperature, pressure and chemical composition under equilibrium state. Unlike conventional thermodynamics, in which entropy, enthalpy, and free energy are defined mathematically in terms of state parameters and thus applicable universally to any system, even without knowing exactly the nature of compound under consideration, statistical thermodynamic analysis must be started from unambiguous a priori modeling of compounds under consideration. When an unrealistic model is chosen at the onset of the statistical thermodynamic approach, the evaluated parameters are without valid physical significance. This inherent nature of the statistical thermodynamic approach might make use of this unique analysis tool somewhat difficult for experimentalists to use casually. However, there also lies a merit of this unique analysis tool to a provide feedback channel to check the validity of the a priori model with reference to the compatibility of the evaluated atomistic interaction parameter values with the macroscopic state parameter values.

The Guest Editor wishes this Special Issue will attract the attention of authors who have been working on entropy and enthalpy aspects of materials science, as well as physicists and chemists using statistical thermodynamics as an analysis tool.

Prof. Dr. Nobumitsu Shohoji
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

  • Statistical thermodynamics
  • Entropy (configurational, electronic)
  • Enthalpy
  • Free Energy
  • Saddle point approach
  • Non-stoichiometry
  • Interstitial
  • Substitutional

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (4 papers)

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Research

17 pages, 1399 KiB  
Article
Knudsen Number Effects on Two-Dimensional Rayleigh–Taylor Instability in Compressible Fluid: Based on a Discrete Boltzmann Method
by Haiyan Ye, Huilin Lai, Demei Li, Yanbiao Gan, Chuandong Lin, Lu Chen and Aiguo Xu
Entropy 2020, 22(5), 500; https://doi.org/10.3390/e22050500 - 26 Apr 2020
Cited by 26 | Viewed by 4412
Abstract
Based on the framework of our previous work [H.L. Lai et al., Phys. Rev. E, 94, 023106 (2016)], we continue to study the effects of Knudsen number on two-dimensional Rayleigh–Taylor (RT) instability in compressible fluid via the discrete Boltzmann method. It is [...] Read more.
Based on the framework of our previous work [H.L. Lai et al., Phys. Rev. E, 94, 023106 (2016)], we continue to study the effects of Knudsen number on two-dimensional Rayleigh–Taylor (RT) instability in compressible fluid via the discrete Boltzmann method. It is found that the Knudsen number effects strongly inhibit the RT instability but always enormously strengthen both the global hydrodynamic non-equilibrium (HNE) and thermodynamic non-equilibrium (TNE) effects. Moreover, when Knudsen number increases, the Kelvin–Helmholtz instability induced by the development of the RT instability is difficult to sufficiently develop in the later stage. Different from the traditional computational fluid dynamics, the discrete Boltzmann method further presents a wealth of non-equilibrium information. Specifically, the two-dimensional TNE quantities demonstrate that, far from the disturbance interface, the value of TNE strength is basically zero; the TNE effects are mainly concentrated on both sides of the interface, which is closely related to the gradient of macroscopic quantities. The global TNE first decreases then increases with evolution. The relevant physical mechanisms are analyzed and discussed. Full article
(This article belongs to the Special Issue Applications of Statistical Thermodynamics)
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13 pages, 530 KiB  
Article
On the Logic of a Prior Based Statistical Mechanics of Polydisperse Systems: The Case of Binary Mixtures
by Fabien Paillusson
Entropy 2019, 21(6), 599; https://doi.org/10.3390/e21060599 - 16 Jun 2019
Cited by 1 | Viewed by 3653
Abstract
Most undergraduate students who have followed a thermodynamics course would have been asked to evaluate the volume occupied by one mole of air under standard conditions of pressure and temperature. However, what is this task exactly referring to? If air is to be [...] Read more.
Most undergraduate students who have followed a thermodynamics course would have been asked to evaluate the volume occupied by one mole of air under standard conditions of pressure and temperature. However, what is this task exactly referring to? If air is to be regarded as a mixture, under what circumstances can this mixture be considered as comprising only one component called “air” in classical statistical mechanics? Furthermore, following the paradigmatic Gibbs’ mixing thought experiment, if one mixes air from a container with air from another container, all other things being equal, should there be a change in entropy? The present paper addresses these questions by developing a prior-based statistical mechanics framework to characterise binary mixtures’ composition realisations and their effect on thermodynamic free energies and entropies. It is found that (a) there exist circumstances for which an ideal binary mixture is thermodynamically equivalent to a single component ideal gas and (b) even when mixing two substances identical in their underlying composition, entropy increase does occur for finite size systems. The nature of the contributions to this increase is then discussed. Full article
(This article belongs to the Special Issue Applications of Statistical Thermodynamics)
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9 pages, 847 KiB  
Article
Entropy, Carnot Cycle, and Information Theory
by Mario Martinelli
Entropy 2019, 21(1), 3; https://doi.org/10.3390/e21010003 - 20 Dec 2018
Cited by 2 | Viewed by 6001
Abstract
The fundamental intuition that Carnot had in analyzing the operation of steam machines is that something remains constant during the reversible thermodynamic cycle. This invariant quantity was later named “entropy” by Clausius. Jaynes proposed a unitary view of thermodynamics and information theory based [...] Read more.
The fundamental intuition that Carnot had in analyzing the operation of steam machines is that something remains constant during the reversible thermodynamic cycle. This invariant quantity was later named “entropy” by Clausius. Jaynes proposed a unitary view of thermodynamics and information theory based on statistical thermodynamics. The unitary vision allows us to analyze the Carnot cycle and to study what happens when the entropy between the beginning and end of the isothermal expansion of the cycle is considered. It is shown that, in connection with a non-zero Kullback–Leibler distance, minor free-energy is available from the cycle. Moreover, the analysis of the adiabatic part of the cycle shows that the internal conversion between energy and work is perturbed by the cost introduced by the code conversion. In summary, the information theoretical tools could help to better understand some details of the cycle and the origin of possible asymmetries. Full article
(This article belongs to the Special Issue Applications of Statistical Thermodynamics)
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19 pages, 394 KiB  
Article
Concavity, Response Functions and Replica Energy
by Alessandro Campa, Lapo Casetti, Ivan Latella, Agustín Pérez-Madrid and Stefano Ruffo
Entropy 2018, 20(12), 907; https://doi.org/10.3390/e20120907 - 28 Nov 2018
Cited by 10 | Viewed by 3591
Abstract
In nonadditive systems, like small systems or like long-range interacting systems even in the thermodynamic limit, ensemble inequivalence can be related to the occurrence of negative response functions, this in turn being connected with anomalous concavity properties of the thermodynamic potentials associated with [...] Read more.
In nonadditive systems, like small systems or like long-range interacting systems even in the thermodynamic limit, ensemble inequivalence can be related to the occurrence of negative response functions, this in turn being connected with anomalous concavity properties of the thermodynamic potentials associated with the various ensembles. We show how the type and number of negative response functions depend on which of the quantities E, V and N (energy, volume and number of particles) are constrained in the ensemble. In particular, we consider the unconstrained ensemble in which E, V and N fluctuate, which is physically meaningful only for nonadditive systems. In fact, its partition function is associated with the replica energy, a thermodynamic function that identically vanishes when additivity holds, but that contains relevant information in nonadditive systems. Full article
(This article belongs to the Special Issue Applications of Statistical Thermodynamics)
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