Boltzmann Entropy, the Holographic Bound and Newtonian Cosmology

[EN] The holographic principle sets an upper bound on the total (Boltzmann) entropy content of the Universe at around 10123kB (kB being Boltzmann¿s constant). In this work we point out the existence of a remarkable duality between nonrelativistic quantum mechanics on the one hand, and Newtonian cosm...

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Autores: Fernández de Córdoba, Pedro|||0000-0002-0347-7280, Isidro, J.M.|||0000-0002-0720-9945
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/126937
Acceso en línea:https://riunet.upv.es/handle/10251/126937
Access Level:acceso abierto
Palabra clave:Gravitational entropy
Holographic principle
Emergent spacetime
MATEMATICA APLICADA
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spelling Boltzmann Entropy, the Holographic Bound and Newtonian CosmologyFernández de Córdoba, Pedro|||0000-0002-0347-7280Isidro, J.M.|||0000-0002-0720-9945Gravitational entropyHolographic principleEmergent spacetimeMATEMATICA APLICADA[EN] The holographic principle sets an upper bound on the total (Boltzmann) entropy content of the Universe at around 10123kB (kB being Boltzmann¿s constant). In this work we point out the existence of a remarkable duality between nonrelativistic quantum mechanics on the one hand, and Newtonian cosmology on the other. Specifically, nonrelativistic quantum mechanics has a quantum probability fluid that exactly mimics the behaviour of the cosmological fluid, the latter considered in the Newtonian approximation. One proves that the equations governing the cosmological fluid (the Euler equation and the continuity equation) become the very equations that govern the quantum probability fluid after applying the Madelung transformation to the Schroedinger wavefunction. Under the assumption that gravitational equipotential surfaces can be identified with isoentropic surfaces, this model allows for a simple computation of the gravitational entropy of a Newtonian Universe.This research was supported by grant no. ENE2015-71333-R (Spain).MDPI AGDepartamento de Matemática AplicadaInstituto Universitario de Matemática Pura y AplicadaEscuela Técnica Superior de Ingeniería IndustrialMinisterio de Economía y EmpresaRepositorio Institucional de la Universitat Politècnica de València Riunet20182018-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/126937reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengMinisterio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 ENE2015-71333-R CONVECCION FORZADA EN CANALES TURBULENTOSopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento (by)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1269372026-06-13T07:49:27Z
dc.title.none.fl_str_mv Boltzmann Entropy, the Holographic Bound and Newtonian Cosmology
title Boltzmann Entropy, the Holographic Bound and Newtonian Cosmology
spellingShingle Boltzmann Entropy, the Holographic Bound and Newtonian Cosmology
Fernández de Córdoba, Pedro|||0000-0002-0347-7280
Gravitational entropy
Holographic principle
Emergent spacetime
MATEMATICA APLICADA
title_short Boltzmann Entropy, the Holographic Bound and Newtonian Cosmology
title_full Boltzmann Entropy, the Holographic Bound and Newtonian Cosmology
title_fullStr Boltzmann Entropy, the Holographic Bound and Newtonian Cosmology
title_full_unstemmed Boltzmann Entropy, the Holographic Bound and Newtonian Cosmology
title_sort Boltzmann Entropy, the Holographic Bound and Newtonian Cosmology
dc.creator.none.fl_str_mv Fernández de Córdoba, Pedro|||0000-0002-0347-7280
Isidro, J.M.|||0000-0002-0720-9945
author Fernández de Córdoba, Pedro|||0000-0002-0347-7280
author_facet Fernández de Córdoba, Pedro|||0000-0002-0347-7280
Isidro, J.M.|||0000-0002-0720-9945
author_role author
author2 Isidro, J.M.|||0000-0002-0720-9945
author2_role author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Instituto Universitario de Matemática Pura y Aplicada
Escuela Técnica Superior de Ingeniería Industrial
Ministerio de Economía y Empresa
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Gravitational entropy
Holographic principle
Emergent spacetime
MATEMATICA APLICADA
topic Gravitational entropy
Holographic principle
Emergent spacetime
MATEMATICA APLICADA
description [EN] The holographic principle sets an upper bound on the total (Boltzmann) entropy content of the Universe at around 10123kB (kB being Boltzmann¿s constant). In this work we point out the existence of a remarkable duality between nonrelativistic quantum mechanics on the one hand, and Newtonian cosmology on the other. Specifically, nonrelativistic quantum mechanics has a quantum probability fluid that exactly mimics the behaviour of the cosmological fluid, the latter considered in the Newtonian approximation. One proves that the equations governing the cosmological fluid (the Euler equation and the continuity equation) become the very equations that govern the quantum probability fluid after applying the Madelung transformation to the Schroedinger wavefunction. Under the assumption that gravitational equipotential surfaces can be identified with isoentropic surfaces, this model allows for a simple computation of the gravitational entropy of a Newtonian Universe.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/126937
url https://riunet.upv.es/handle/10251/126937
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 ENE2015-71333-R CONVECCION FORZADA EN CANALES TURBULENTOS
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv MDPI AG
publisher.none.fl_str_mv MDPI AG
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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