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Generalized Statistical Thermodynamics
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Generalized Statistical Thermodynamics

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

Deadline for manuscript submissions: closed (30 September 2020) | Viewed by 11280

Special Issue Editors

Prof. Dr. Themis Matsoukas

E-Mail Website
Guest Editor
Department of Chemical Engineering, Pennsylvania State University, 313 Chemical and Biomedical Engineering Building, University Park, PA 16802, USA
Interests: statisitical thermodynamics; population balances and their application to multicomponent systems; deterministic and stochastic simulation of particulate processes; clustering and fragmentation on discrete graphs; statistical mechanics of stochastic processes; nanocolloids and aerosols
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Milton W. Cole

E-Mail Website
Guest Editor
Department of Physics, Penn State University, 104 Davey Lab, University Park, PA 16802, USA
Interests: statistical mechanics; adsorption primary; statistical physics; climate change; medical physics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Statistical thermodynamics, undoubtedly one of the most important achievements in mathematical physics, is the rigorous mathematical language that describes the equilibrium state of a system of interacting particles, classical or quantum. Its appeal, however, extends beyond molecular systems to generic stochastic populations, whether these are colloidal particles, ecological systems or financial markets. At its most fundamental level, statistical thermodynamics is a variational calculus of the most probable distribution: Out of all possible distributions, the one that materializes as the macroscopic observable is the most probable distribution.

This Special Issue solicits contributions that apply the language and tools of statistical thermodynamics to systems beyond molecules. Areas of special interest include clustering and fragmentation in particulate systems, propagation and extinction of epidemics, statistical thermodynamics of networks, and the application of statistical mechanics to stochastic processes in general.

Prof. Dr. Themis Matsoukas
Prof. Dr. Milton W. Cole
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 mechanics
  • population balances
  • stochastic processes
  • most probable distribution

Published Papers (4 papers)

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Research

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26 pages, 456 KiB  
Article
The Smoluchowski Ensemble—Statistical Mechanics of Aggregation
by Themis Matsoukas
Entropy 2020, 22(10), 1181; https://doi.org/10.3390/e22101181 - 20 Oct 2020
Cited by 5 | Viewed by 3538
Abstract
We present a rigorous thermodynamic treatment of irreversible binary aggregation. We construct the Smoluchowski ensemble as the set of discrete finite distributions that are reached in fixed number of merging events and define a probability measure on this ensemble, such that the mean [...] Read more.
We present a rigorous thermodynamic treatment of irreversible binary aggregation. We construct the Smoluchowski ensemble as the set of discrete finite distributions that are reached in fixed number of merging events and define a probability measure on this ensemble, such that the mean distribution in the mean-field approximation is governed by the Smoluchowski equation. In the scaling limit this ensemble gives rise to a set of relationships identical to those of familiar statistical thermodynamics. The central element of the thermodynamic treatment is the selection functional, a functional of feasible distributions that connects the probability of distribution to the details of the aggregation model. We obtain scaling expressions for general kernels and closed-form results for the special case of the constant, sum and product kernel. We study the stability of the most probable distribution, provide criteria for the sol-gel transition and obtain the distribution in the post-gel region by simple thermodynamic arguments. Full article
(This article belongs to the Special Issue Generalized Statistical Thermodynamics)
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16 pages, 1308 KiB  
Article
Network Rewiring in the r-K Plane
by Maria Letizia Bertotti and Giovanni Modanese
Entropy 2020, 22(6), 653; https://doi.org/10.3390/e22060653 - 13 Jun 2020
Cited by 4 | Viewed by 1859
Abstract
We generate correlated scale-free networks in the configuration model through a new rewiring algorithm that allows one to tune the Newman assortativity coefficient r and the average degree of the nearest neighbors K (in the range − 1 ≤ r ≤ 1 , [...] Read more.
We generate correlated scale-free networks in the configuration model through a new rewiring algorithm that allows one to tune the Newman assortativity coefficient r and the average degree of the nearest neighbors K (in the range − 1 ≤ r ≤ 1 , K ≥ ⟨ k ⟩ ). At each attempted rewiring step, local variations Δ r and Δ K are computed and then the step is accepted according to a standard Metropolis probability exp ( ± Δ r / T ) , where T is a variable temperature. We prove a general relation between Δ r and Δ K , thus finding a connection between two variables that have very different definitions and topological meaning. We describe rewiring trajectories in the r-K plane and explore the limits of maximally assortative and disassortative networks, including the case of small minimum degree ( k m i n ≥ 1 ), which has previously not been considered. The size of the giant component and the entropy of the network are monitored in the rewiring. The average number of second neighbors in the branching approximation z ¯ 2 , B is proven to be constant in the rewiring, and independent from the correlations for Markovian networks. As a function of the degree, however, the number of second neighbors gives useful information on the network connectivity and is also monitored. Full article
(This article belongs to the Special Issue Generalized Statistical Thermodynamics)
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7 pages, 384 KiB  
Article
Ensembles of Atoms, Ensembles of Species: Comparative Statistical Mechanics
by Michael G. Bowler
Entropy 2020, 22(6), 610; https://doi.org/10.3390/e22060610 - 30 May 2020
Cited by 1 | Viewed by 1656
Abstract
The methods of statistical physics are exemplified in the classical perfect gas—each atom is a single dynamical entity. Such methods can be applied in ecology to the distribution of cosmopolitan species over many sites. The analogue of an atom is a class of [...] Read more.
The methods of statistical physics are exemplified in the classical perfect gas—each atom is a single dynamical entity. Such methods can be applied in ecology to the distribution of cosmopolitan species over many sites. The analogue of an atom is a class of species distinguished by the number of sites at which it occurs, hardly a material entity; yet, the methods of statistical physics nonetheless seem applicable. This paper compares the application of statistical mechanics to the distribution of atoms and to the vastly different problem of distribution of cosmopolitan species. A number of different approaches show that these distributed entities must be in some sense equivalent; the dynamics must be controlled by interaction between species and the global environment rather than between species and many uncorrelated local environments. Full article
(This article belongs to the Special Issue Generalized Statistical Thermodynamics)
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Review

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42 pages, 1618 KiB  
Review
Thermodynamic Formalism in Neuronal Dynamics and Spike Train Statistics
by Rodrigo Cofré, Cesar Maldonado and Bruno Cessac
Entropy 2020, 22(11), 1330; https://doi.org/10.3390/e22111330 - 23 Nov 2020
Cited by 6 | Viewed by 3619
Abstract
The Thermodynamic Formalism provides a rigorous mathematical framework for studying quantitative and qualitative aspects of dynamical systems. At its core, there is a variational principle that corresponds, in its simplest form, to the Maximum Entropy principle. It is used as a statistical inference [...] Read more.
The Thermodynamic Formalism provides a rigorous mathematical framework for studying quantitative and qualitative aspects of dynamical systems. At its core, there is a variational principle that corresponds, in its simplest form, to the Maximum Entropy principle. It is used as a statistical inference procedure to represent, by specific probability measures (Gibbs measures), the collective behaviour of complex systems. This framework has found applications in different domains of science. In particular, it has been fruitful and influential in neurosciences. In this article, we review how the Thermodynamic Formalism can be exploited in the field of theoretical neuroscience, as a conceptual and operational tool, in order to link the dynamics of interacting neurons and the statistics of action potentials from either experimental data or mathematical models. We comment on perspectives and open problems in theoretical neuroscience that could be addressed within this formalism. Full article
(This article belongs to the Special Issue Generalized Statistical Thermodynamics)
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