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Combinatorics and Statistical Mechanics of Integer Partitions

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 o...

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Detalles Bibliográficos
Autor principal: Matsoukas, Themis
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9955035/
https://www.ncbi.nlm.nih.gov/pubmed/36832751
http://dx.doi.org/10.3390/e25020385
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author Matsoukas, Themis
author_facet Matsoukas, Themis
author_sort Matsoukas, Themis
collection PubMed
description 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.
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spelling pubmed-99550352023-02-25 Combinatorics and Statistical Mechanics of Integer Partitions Matsoukas, Themis Entropy (Basel) Article 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. MDPI 2023-02-20 /pmc/articles/PMC9955035/ /pubmed/36832751 http://dx.doi.org/10.3390/e25020385 Text en © 2023 by the author. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Matsoukas, Themis
Combinatorics and Statistical Mechanics of Integer Partitions
title Combinatorics and Statistical Mechanics of Integer Partitions
title_full Combinatorics and Statistical Mechanics of Integer Partitions
title_fullStr Combinatorics and Statistical Mechanics of Integer Partitions
title_full_unstemmed Combinatorics and Statistical Mechanics of Integer Partitions
title_short Combinatorics and Statistical Mechanics of Integer Partitions
title_sort combinatorics and statistical mechanics of integer partitions
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9955035/
https://www.ncbi.nlm.nih.gov/pubmed/36832751
http://dx.doi.org/10.3390/e25020385
work_keys_str_mv AT matsoukasthemis combinatoricsandstatisticalmechanicsofintegerpartitions