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Rényi Entropy in Statistical Mechanics

Rényi entropy was originally introduced in the field of information theory as a parametric relaxation of Shannon (in physics, Boltzmann–Gibbs) entropy. This has also fuelled different attempts to generalise statistical mechanics, although mostly skipping the physical arguments behind this entropy an...

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Autores principales: Fuentes, Jesús, Gonçalves, Jorge
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9407421/
https://www.ncbi.nlm.nih.gov/pubmed/36010744
http://dx.doi.org/10.3390/e24081080
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author Fuentes, Jesús
Gonçalves, Jorge
author_facet Fuentes, Jesús
Gonçalves, Jorge
author_sort Fuentes, Jesús
collection PubMed
description Rényi entropy was originally introduced in the field of information theory as a parametric relaxation of Shannon (in physics, Boltzmann–Gibbs) entropy. This has also fuelled different attempts to generalise statistical mechanics, although mostly skipping the physical arguments behind this entropy and instead tending to introduce it artificially. However, as we will show, modifications to the theory of statistical mechanics are needless to see how Rényi entropy automatically arises as the average rate of change of free energy over an ensemble at different temperatures. Moreover, this notion is extended by considering distributions for isospectral, non-isothermal processes, resulting in relative versions of free energy, in which the Kullback–Leibler divergence or the relative version of Rényi entropy appear within the structure of the corrections to free energy. These generalisations of free energy recover the ordinary thermodynamic potential whenever isothermal processes are considered.
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spelling pubmed-94074212022-08-26 Rényi Entropy in Statistical Mechanics Fuentes, Jesús Gonçalves, Jorge Entropy (Basel) Article Rényi entropy was originally introduced in the field of information theory as a parametric relaxation of Shannon (in physics, Boltzmann–Gibbs) entropy. This has also fuelled different attempts to generalise statistical mechanics, although mostly skipping the physical arguments behind this entropy and instead tending to introduce it artificially. However, as we will show, modifications to the theory of statistical mechanics are needless to see how Rényi entropy automatically arises as the average rate of change of free energy over an ensemble at different temperatures. Moreover, this notion is extended by considering distributions for isospectral, non-isothermal processes, resulting in relative versions of free energy, in which the Kullback–Leibler divergence or the relative version of Rényi entropy appear within the structure of the corrections to free energy. These generalisations of free energy recover the ordinary thermodynamic potential whenever isothermal processes are considered. MDPI 2022-08-05 /pmc/articles/PMC9407421/ /pubmed/36010744 http://dx.doi.org/10.3390/e24081080 Text en © 2022 by the authors. 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
Fuentes, Jesús
Gonçalves, Jorge
Rényi Entropy in Statistical Mechanics
title Rényi Entropy in Statistical Mechanics
title_full Rényi Entropy in Statistical Mechanics
title_fullStr Rényi Entropy in Statistical Mechanics
title_full_unstemmed Rényi Entropy in Statistical Mechanics
title_short Rényi Entropy in Statistical Mechanics
title_sort rényi entropy in statistical mechanics
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9407421/
https://www.ncbi.nlm.nih.gov/pubmed/36010744
http://dx.doi.org/10.3390/e24081080
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