Thermodynamic equilibrium in general relativity

Autores
Lima, J. A. S.; Del Popolo, A.; Plastino, Ángel Ricardo
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The thermodynamic equilibrium condition for a static self-gravitating fluid in the Einstein theory is defined by the Tolman-Ehrenfest temperature law, Tg00(xi)=constant, according to which the proper temperature depends explicitly on the position within the medium through the metric coefficient g00(xi). By assuming the validity of Tolman-Ehrenfest "pocket temperature," Klein also proved a similar relation for the chemical potential, namely, μg00(xi)=constant. In this paper we prove that a more general relation uniting both quantities holds regardless of the equation of state satisfied by the medium, and that the original Tolman-Ehrenfest law form is valid only if the chemical potential vanishes identically. In the general case of equilibrium, the temperature and the chemical potential are intertwined in such a way that only a definite (position dependent) relation uniting both quantities is obeyed. As an illustration of these results, the temperature expressions for an isothermal gas (finite spherical distribution) and a neutron star are also determined.
Fil: Lima, J. A. S.. Universidade de Sao Paulo; Brasil
Fil: Del Popolo, A.. Università Degli Studi Di Catania; Italia
Fil: Plastino, Ángel Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Noroeste de la Provincia de Buenos Aires; Argentina
Materia
Thermodynamic Equilibrium
General Relativity
Tolman-Ehrenfest temperature
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/175160
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/175160
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network_name_str CONICET Digital (CONICET)
spelling Thermodynamic equilibrium in general relativityLima, J. A. S.Del Popolo, A.Plastino, Ángel RicardoThermodynamic EquilibriumGeneral RelativityTolman-Ehrenfest temperaturehttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The thermodynamic equilibrium condition for a static self-gravitating fluid in the Einstein theory is defined by the Tolman-Ehrenfest temperature law, Tg00(xi)=constant, according to which the proper temperature depends explicitly on the position within the medium through the metric coefficient g00(xi). By assuming the validity of Tolman-Ehrenfest "pocket temperature," Klein also proved a similar relation for the chemical potential, namely, μg00(xi)=constant. In this paper we prove that a more general relation uniting both quantities holds regardless of the equation of state satisfied by the medium, and that the original Tolman-Ehrenfest law form is valid only if the chemical potential vanishes identically. In the general case of equilibrium, the temperature and the chemical potential are intertwined in such a way that only a definite (position dependent) relation uniting both quantities is obeyed. As an illustration of these results, the temperature expressions for an isothermal gas (finite spherical distribution) and a neutron star are also determined.Fil: Lima, J. A. S.. Universidade de Sao Paulo; BrasilFil: Del Popolo, A.. Università Degli Studi Di Catania; ItaliaFil: Plastino, Ángel Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Noroeste de la Provincia de Buenos Aires; ArgentinaAmerican Physical Society2019-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/175160Lima, J. A. S.; Del Popolo, A.; Plastino, Ángel Ricardo; Thermodynamic equilibrium in general relativity; American Physical Society; Physical Review D; 100; 10; 11-2019; 1-72470-00102470-0029CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevD.100.104042info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:50:56Zoai:ri.conicet.gov.ar:11336/175160instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-15 14:50:57.04CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Thermodynamic equilibrium in general relativity
title Thermodynamic equilibrium in general relativity
spellingShingle Thermodynamic equilibrium in general relativity
Lima, J. A. S.
Thermodynamic Equilibrium
General Relativity
Tolman-Ehrenfest temperature
title_short Thermodynamic equilibrium in general relativity
title_full Thermodynamic equilibrium in general relativity
title_fullStr Thermodynamic equilibrium in general relativity
title_full_unstemmed Thermodynamic equilibrium in general relativity
title_sort Thermodynamic equilibrium in general relativity
dc.creator.none.fl_str_mv Lima, J. A. S.
Del Popolo, A.
Plastino, Ángel Ricardo
author Lima, J. A. S.
author_facet Lima, J. A. S.
Del Popolo, A.
Plastino, Ángel Ricardo
author_role author
author2 Del Popolo, A.
Plastino, Ángel Ricardo
author2_role author
author
dc.subject.none.fl_str_mv Thermodynamic Equilibrium
General Relativity
Tolman-Ehrenfest temperature
topic Thermodynamic Equilibrium
General Relativity
Tolman-Ehrenfest temperature
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The thermodynamic equilibrium condition for a static self-gravitating fluid in the Einstein theory is defined by the Tolman-Ehrenfest temperature law, Tg00(xi)=constant, according to which the proper temperature depends explicitly on the position within the medium through the metric coefficient g00(xi). By assuming the validity of Tolman-Ehrenfest "pocket temperature," Klein also proved a similar relation for the chemical potential, namely, μg00(xi)=constant. In this paper we prove that a more general relation uniting both quantities holds regardless of the equation of state satisfied by the medium, and that the original Tolman-Ehrenfest law form is valid only if the chemical potential vanishes identically. In the general case of equilibrium, the temperature and the chemical potential are intertwined in such a way that only a definite (position dependent) relation uniting both quantities is obeyed. As an illustration of these results, the temperature expressions for an isothermal gas (finite spherical distribution) and a neutron star are also determined.
Fil: Lima, J. A. S.. Universidade de Sao Paulo; Brasil
Fil: Del Popolo, A.. Università Degli Studi Di Catania; Italia
Fil: Plastino, Ángel Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Noroeste de la Provincia de Buenos Aires; Argentina
description The thermodynamic equilibrium condition for a static self-gravitating fluid in the Einstein theory is defined by the Tolman-Ehrenfest temperature law, Tg00(xi)=constant, according to which the proper temperature depends explicitly on the position within the medium through the metric coefficient g00(xi). By assuming the validity of Tolman-Ehrenfest "pocket temperature," Klein also proved a similar relation for the chemical potential, namely, μg00(xi)=constant. In this paper we prove that a more general relation uniting both quantities holds regardless of the equation of state satisfied by the medium, and that the original Tolman-Ehrenfest law form is valid only if the chemical potential vanishes identically. In the general case of equilibrium, the temperature and the chemical potential are intertwined in such a way that only a definite (position dependent) relation uniting both quantities is obeyed. As an illustration of these results, the temperature expressions for an isothermal gas (finite spherical distribution) and a neutron star are also determined.
publishDate 2019
dc.date.none.fl_str_mv 2019-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/175160
Lima, J. A. S.; Del Popolo, A.; Plastino, Ángel Ricardo; Thermodynamic equilibrium in general relativity; American Physical Society; Physical Review D; 100; 10; 11-2019; 1-7
2470-0010
2470-0029
CONICET Digital
CONICET
url http://hdl.handle.net/11336/175160
identifier_str_mv Lima, J. A. S.; Del Popolo, A.; Plastino, Ángel Ricardo; Thermodynamic equilibrium in general relativity; American Physical Society; Physical Review D; 100; 10; 11-2019; 1-7
2470-0010
2470-0029
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevD.100.104042
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1846083034707656704
score 12.891075

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