Statistical mechanics of few-particle systems: Exact results for two useful models

Autores
Miranda, Enrique Nestor
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The statistical mechanics of small clusters (n ∼ 10-50 elements) of harmonic oscillators and two-level systems is studied exactly, following the microcanonical, canonical and grand canonical formalisms. For clusters with several hundred particles, the results from the three formalisms coincide with those found in the thermodynamic limit. However, for clusters formed by a few tens of elements, the three ensembles yield different results. For a cluster with a few tens of harmonic oscillators, when the heat capacity per oscillator is evaluated within the canonical formalism, it reaches a limit value equal to k B, as in the thermodynamic case, while within the microcanonical formalism the limit value is k B(1-1/n). This difference could be measured experimentally. For a cluster with a few tens of two-level systems, the heat capacity evaluated within the canonical and microcanonical ensembles also presents differences that could be detected experimentally. Both the microcanonical and grand canonical formalism show that the entropy is non-additive for systems this small, while the canonical ensemble reaches the opposite conclusion. These results suggest that the microcanonical ensemble is the most appropriate for dealing with systems with tens of particles.
Fil: Miranda, Enrique Nestor. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Provincia de Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Universidad Nacional de Cuyo. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales; Argentina
Materia
Ensembles
Few-Particle Systems
Specific Heat Nanoparticles
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:11336/57118
Acceder
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spelling Statistical mechanics of few-particle systems: Exact results for two useful modelsMiranda, Enrique NestorEnsemblesFew-Particle SystemsSpecific Heat Nanoparticleshttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The statistical mechanics of small clusters (n ∼ 10-50 elements) of harmonic oscillators and two-level systems is studied exactly, following the microcanonical, canonical and grand canonical formalisms. For clusters with several hundred particles, the results from the three formalisms coincide with those found in the thermodynamic limit. However, for clusters formed by a few tens of elements, the three ensembles yield different results. For a cluster with a few tens of harmonic oscillators, when the heat capacity per oscillator is evaluated within the canonical formalism, it reaches a limit value equal to k B, as in the thermodynamic case, while within the microcanonical formalism the limit value is k B(1-1/n). This difference could be measured experimentally. For a cluster with a few tens of two-level systems, the heat capacity evaluated within the canonical and microcanonical ensembles also presents differences that could be detected experimentally. Both the microcanonical and grand canonical formalism show that the entropy is non-additive for systems this small, while the canonical ensemble reaches the opposite conclusion. These results suggest that the microcanonical ensemble is the most appropriate for dealing with systems with tens of particles.Fil: Miranda, Enrique Nestor. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Provincia de Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Universidad Nacional de Cuyo. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales; ArgentinaIOP Publishing2017-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/57118Miranda, Enrique Nestor; Statistical mechanics of few-particle systems: Exact results for two useful models; IOP Publishing; European Journal of Physics; 38; 6; 11-2017; 1-60143-0807CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/article/10.1088/1361-6404/aa82fa/metainfo:eu-repo/semantics/altIdentifier/doi/10.1088/1361-6404/aa82fainfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:50:20Zoai:ri.conicet.gov.ar:11336/57118instacron: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:34982025-09-03 09:50:20.302CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Statistical mechanics of few-particle systems: Exact results for two useful models
title Statistical mechanics of few-particle systems: Exact results for two useful models
spellingShingle Statistical mechanics of few-particle systems: Exact results for two useful models
Miranda, Enrique Nestor
Ensembles
Few-Particle Systems
Specific Heat Nanoparticles
title_short Statistical mechanics of few-particle systems: Exact results for two useful models
title_full Statistical mechanics of few-particle systems: Exact results for two useful models
title_fullStr Statistical mechanics of few-particle systems: Exact results for two useful models
title_full_unstemmed Statistical mechanics of few-particle systems: Exact results for two useful models
title_sort Statistical mechanics of few-particle systems: Exact results for two useful models
dc.creator.none.fl_str_mv Miranda, Enrique Nestor
author Miranda, Enrique Nestor
author_facet Miranda, Enrique Nestor
author_role author
dc.subject.none.fl_str_mv Ensembles
Few-Particle Systems
Specific Heat Nanoparticles
topic Ensembles
Few-Particle Systems
Specific Heat Nanoparticles
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 statistical mechanics of small clusters (n ∼ 10-50 elements) of harmonic oscillators and two-level systems is studied exactly, following the microcanonical, canonical and grand canonical formalisms. For clusters with several hundred particles, the results from the three formalisms coincide with those found in the thermodynamic limit. However, for clusters formed by a few tens of elements, the three ensembles yield different results. For a cluster with a few tens of harmonic oscillators, when the heat capacity per oscillator is evaluated within the canonical formalism, it reaches a limit value equal to k B, as in the thermodynamic case, while within the microcanonical formalism the limit value is k B(1-1/n). This difference could be measured experimentally. For a cluster with a few tens of two-level systems, the heat capacity evaluated within the canonical and microcanonical ensembles also presents differences that could be detected experimentally. Both the microcanonical and grand canonical formalism show that the entropy is non-additive for systems this small, while the canonical ensemble reaches the opposite conclusion. These results suggest that the microcanonical ensemble is the most appropriate for dealing with systems with tens of particles.
Fil: Miranda, Enrique Nestor. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Provincia de Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Universidad Nacional de Cuyo. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales; Argentina
description The statistical mechanics of small clusters (n ∼ 10-50 elements) of harmonic oscillators and two-level systems is studied exactly, following the microcanonical, canonical and grand canonical formalisms. For clusters with several hundred particles, the results from the three formalisms coincide with those found in the thermodynamic limit. However, for clusters formed by a few tens of elements, the three ensembles yield different results. For a cluster with a few tens of harmonic oscillators, when the heat capacity per oscillator is evaluated within the canonical formalism, it reaches a limit value equal to k B, as in the thermodynamic case, while within the microcanonical formalism the limit value is k B(1-1/n). This difference could be measured experimentally. For a cluster with a few tens of two-level systems, the heat capacity evaluated within the canonical and microcanonical ensembles also presents differences that could be detected experimentally. Both the microcanonical and grand canonical formalism show that the entropy is non-additive for systems this small, while the canonical ensemble reaches the opposite conclusion. These results suggest that the microcanonical ensemble is the most appropriate for dealing with systems with tens of particles.
publishDate 2017
dc.date.none.fl_str_mv 2017-11
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/11336/57118
Miranda, Enrique Nestor; Statistical mechanics of few-particle systems: Exact results for two useful models; IOP Publishing; European Journal of Physics; 38; 6; 11-2017; 1-6
0143-0807
CONICET Digital
CONICET
url http://hdl.handle.net/11336/57118
identifier_str_mv Miranda, Enrique Nestor; Statistical mechanics of few-particle systems: Exact results for two useful models; IOP Publishing; European Journal of Physics; 38; 6; 11-2017; 1-6
0143-0807
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/article/10.1088/1361-6404/aa82fa/meta
info:eu-repo/semantics/altIdentifier/doi/10.1088/1361-6404/aa82fa
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 IOP Publishing
publisher.none.fl_str_mv IOP Publishing
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
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score 13.13397

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