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Generalized Statistical Thermodynamics II

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

Deadline for manuscript submissions: closed (31 August 2023) | Viewed by 2865

Special Issue Editors


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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

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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,

Population balances deal with the evolution of a distributed property, trait, or other characteristic over the members of a population. Numerous examples are covered under this generic description, from colloidal particles and cells at the microscale, to plants and animals at the macroscale, to stars and galaxies at astronomical scales. Stochastic population balances model the evolution of the population as a stochastic process that considers all possible transitions of state at any given moment.

This Special Issue invites papers that apply the tools and formalism of statistical mechanics to the evolution of stochastic populations. Areas of special interest include clustering and fragmentation in particulate systems, propagation and extinction of epidemics, statistical thermodynamics of networks, evolution of biological populations, and generally problems that view the evolution of populations as a random walk in the event space of possible states.

Prof. Dr. Themis Matsoukas
Prof. Dr. Milton W. Cole
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.

Published Papers (2 papers)

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15 pages, 1730 KiB  
Article
Arbitrage Equilibrium, Invariance, and the Emergence of Spontaneous Order in the Dynamics of Bird-like Agents
by Abhishek Sivaram and Venkat Venkatasubramanian
Entropy 2023, 25(7), 1043; https://doi.org/10.3390/e25071043 - 11 Jul 2023
Cited by 2 | Viewed by 697
Abstract
The physics of active biological matter, such as bacterial colonies and bird flocks, exhibiting interesting self-organizing dynamical behavior has gained considerable importance in recent years. Current theoretical advances use techniques from hydrodynamics, kinetic theory, and non-equilibrium statistical physics. However, for biological agents, these [...] Read more.
The physics of active biological matter, such as bacterial colonies and bird flocks, exhibiting interesting self-organizing dynamical behavior has gained considerable importance in recent years. Current theoretical advances use techniques from hydrodynamics, kinetic theory, and non-equilibrium statistical physics. However, for biological agents, these approaches do not seem to recognize explicitly their critical feature: namely, the role of survival-driven purpose and the attendant pursuit of maximum utility. Here, we propose a game-theoretic framework, statistical teleodynamics, that demonstrates that the bird-like agents self-organize dynamically into flocks to approach a stable arbitrage equilibriumof equal effective utilities. This is essentially the invisible handmechanism of Adam Smith’s in an ecological context. What we demonstrate is for ideal systems, similar to the ideal gas or Ising model in thermodynamics. The next steps would involve examining and learning how real swarms behave compared to their ideal versions. Our theory is not limited to just birds flocking but can be adapted for the self-organizing dynamics of other active matter systems. Full article
(This article belongs to the Special Issue Generalized Statistical Thermodynamics II)
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15 pages, 794 KiB  
Article
Combinatorics and Statistical Mechanics of Integer Partitions
by Themis Matsoukas
Entropy 2023, 25(2), 385; https://doi.org/10.3390/e25020385 - 20 Feb 2023
Cited by 1 | Viewed by 1542
Abstract
We study the set of integer partitions as a probability space that generates distributions and, in the asymptotic limit, obeys thermodynamics. We view ordered integer partition as a configuration of cluster masses and associate them with the distribution of masses it contains. We [...] Read more.
We study the set of integer partitions as a probability space that generates distributions and, in the asymptotic limit, obeys thermodynamics. We view ordered integer partition as a configuration of cluster masses and associate them with the distribution of masses it contains. We organized the set of ordered partitions into a table that forms a microcanonical ensemble and whose columns form a set of canonical ensembles. We define a functional of the distribution (selection functional) that establishes a probability measure on the distributions of the ensemble, study the combinatorial properties of this space, define its partition functions, and show that, in the asymptotic limit, this space obeys thermodynamics. We construct a stochastic process that we call exchange reaction and used it to sample the mean distribution by Mote Carlo simulation. We demonstrated that, with appropriate choice of the selection functional, we can obtain any distribution as the equilibrium distribution of the ensemble. Full article
(This article belongs to the Special Issue Generalized Statistical Thermodynamics II)
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