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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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Formato: | Online Artículo Texto |
Lenguaje: | English |
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MDPI
2023
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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. |
format | Online Article Text |
id | pubmed-9955035 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
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 |