Statistical mechanical theory of an oscillating isolated system: The relaxation to equilibrium

In this Contribution we show that a suitably defined nonequilibrium entropy of an N-body isolated system is not a constant of the motion, in general, and its variation is bounded, the bounds determined by the thermodynamic entropy, i.e., the equilibrium entropy. We define the nonequilibrium entropy...

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Detalhes bibliográficos
Autor: Pérez Madrid, Agustín
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2007
País:España
Recursos:Universidad de Barcelona
Repositório:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/24584
Acesso em linha:https://hdl.handle.net/2445/24584
Access Level:Acceso aberto
Palavra-chave:Mecànica estadística
Processos estocàstics
Entropia
Termodinàmica
Equació de Fokker-Planck
Statistical mechanics
Stochastic processes
Entropy
Thermodynamics
Fokker-Planck equation
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spelling Statistical mechanical theory of an oscillating isolated system: The relaxation to equilibriumPérez Madrid, AgustínMecànica estadísticaProcessos estocàsticsEntropiaTermodinàmicaEquació de Fokker-PlanckStatistical mechanicsStochastic processesEntropyThermodynamicsFokker-Planck equationIn this Contribution we show that a suitably defined nonequilibrium entropy of an N-body isolated system is not a constant of the motion, in general, and its variation is bounded, the bounds determined by the thermodynamic entropy, i.e., the equilibrium entropy. We define the nonequilibrium entropy as a convex functional of the set of n-particle reduced distribution functions (n ? N) generalizing the Gibbs fine-grained entropy formula. Additionally, as a consequence of our microscopic analysis we find that this nonequilibrium entropy behaves as a free entropic oscillator. In the approach to the equilibrium regime, we find relaxation equations of the Fokker-Planck type, particularly for the one-particle distribution function.American Institute of Physics2007info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2445/24584Articles publicats en revistes (Física de la Matèria Condensada)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésReproducció del document proporcionada per AIP i http://dx.doi.org/10.1063/1.2800165Journal of Mathematical Physics, 2007, vol. 48, p. 103302http://dx.doi.org/10.1063/1.2800165(c) American Institute of Physics, 2007info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/245842026-05-27T06:46:51Z
dc.title.none.fl_str_mv Statistical mechanical theory of an oscillating isolated system: The relaxation to equilibrium
title Statistical mechanical theory of an oscillating isolated system: The relaxation to equilibrium
spellingShingle Statistical mechanical theory of an oscillating isolated system: The relaxation to equilibrium
Pérez Madrid, Agustín
Mecànica estadística
Processos estocàstics
Entropia
Termodinàmica
Equació de Fokker-Planck
Statistical mechanics
Stochastic processes
Entropy
Thermodynamics
Fokker-Planck equation
title_short Statistical mechanical theory of an oscillating isolated system: The relaxation to equilibrium
title_full Statistical mechanical theory of an oscillating isolated system: The relaxation to equilibrium
title_fullStr Statistical mechanical theory of an oscillating isolated system: The relaxation to equilibrium
title_full_unstemmed Statistical mechanical theory of an oscillating isolated system: The relaxation to equilibrium
title_sort Statistical mechanical theory of an oscillating isolated system: The relaxation to equilibrium
dc.creator.none.fl_str_mv Pérez Madrid, Agustín
author Pérez Madrid, Agustín
author_facet Pérez Madrid, Agustín
author_role author
dc.subject.none.fl_str_mv Mecànica estadística
Processos estocàstics
Entropia
Termodinàmica
Equació de Fokker-Planck
Statistical mechanics
Stochastic processes
Entropy
Thermodynamics
Fokker-Planck equation
topic Mecànica estadística
Processos estocàstics
Entropia
Termodinàmica
Equació de Fokker-Planck
Statistical mechanics
Stochastic processes
Entropy
Thermodynamics
Fokker-Planck equation
description In this Contribution we show that a suitably defined nonequilibrium entropy of an N-body isolated system is not a constant of the motion, in general, and its variation is bounded, the bounds determined by the thermodynamic entropy, i.e., the equilibrium entropy. We define the nonequilibrium entropy as a convex functional of the set of n-particle reduced distribution functions (n ? N) generalizing the Gibbs fine-grained entropy formula. Additionally, as a consequence of our microscopic analysis we find that this nonequilibrium entropy behaves as a free entropic oscillator. In the approach to the equilibrium regime, we find relaxation equations of the Fokker-Planck type, particularly for the one-particle distribution function.
publishDate 2007
dc.date.none.fl_str_mv 2007
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/24584
url https://hdl.handle.net/2445/24584
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document proporcionada per AIP i http://dx.doi.org/10.1063/1.2800165
Journal of Mathematical Physics, 2007, vol. 48, p. 103302
http://dx.doi.org/10.1063/1.2800165
dc.rights.none.fl_str_mv (c) American Institute of Physics, 2007
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) American Institute of Physics, 2007
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv American Institute of Physics
publisher.none.fl_str_mv American Institute of Physics
dc.source.none.fl_str_mv Articles publicats en revistes (Física de la Matèria Condensada)
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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