The Shannon–McMillan Theorem Proves Convergence to Equiprobability of Boltzmann’s Microstates

This paper shows that, for a large number of particles and for distinguishable and non-interacting identical particles, convergence to equiprobability of the W microstates of the famous Boltzmann–Planck entropy formula S = k log(W) is proved by the Shannon–McMillan theorem, a cornerstone of informat...

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Detalles Bibliográficos
Autor principal: Spalvieri, Arnaldo
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8306686/
https://www.ncbi.nlm.nih.gov/pubmed/34356440
http://dx.doi.org/10.3390/e23070899
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author Spalvieri, Arnaldo
author_facet Spalvieri, Arnaldo
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description This paper shows that, for a large number of particles and for distinguishable and non-interacting identical particles, convergence to equiprobability of the W microstates of the famous Boltzmann–Planck entropy formula S = k log(W) is proved by the Shannon–McMillan theorem, a cornerstone of information theory. This result further strengthens the link between information theory and statistical mechanics.
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spelling pubmed-83066862021-07-25 The Shannon–McMillan Theorem Proves Convergence to Equiprobability of Boltzmann’s Microstates Spalvieri, Arnaldo Entropy (Basel) Article This paper shows that, for a large number of particles and for distinguishable and non-interacting identical particles, convergence to equiprobability of the W microstates of the famous Boltzmann–Planck entropy formula S = k log(W) is proved by the Shannon–McMillan theorem, a cornerstone of information theory. This result further strengthens the link between information theory and statistical mechanics. MDPI 2021-07-15 /pmc/articles/PMC8306686/ /pubmed/34356440 http://dx.doi.org/10.3390/e23070899 Text en © 2021 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
Spalvieri, Arnaldo
The Shannon–McMillan Theorem Proves Convergence to Equiprobability of Boltzmann’s Microstates
title The Shannon–McMillan Theorem Proves Convergence to Equiprobability of Boltzmann’s Microstates
title_full The Shannon–McMillan Theorem Proves Convergence to Equiprobability of Boltzmann’s Microstates
title_fullStr The Shannon–McMillan Theorem Proves Convergence to Equiprobability of Boltzmann’s Microstates
title_full_unstemmed The Shannon–McMillan Theorem Proves Convergence to Equiprobability of Boltzmann’s Microstates
title_short The Shannon–McMillan Theorem Proves Convergence to Equiprobability of Boltzmann’s Microstates
title_sort shannon–mcmillan theorem proves convergence to equiprobability of boltzmann’s microstates
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8306686/
https://www.ncbi.nlm.nih.gov/pubmed/34356440
http://dx.doi.org/10.3390/e23070899
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