Rényi entropies in the n →0 limit and entanglement temperatures

Autores
Agón, Cesar A.; Casini, Horacio German; Martinez, Pedro Jorge
Año de publicación
2023
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Entanglement temperatures (ET) are a generalization of Unruh temperatures valid for states reduced to any region of space. They encode in a thermal fashion the high energy behavior of the state around a point. These temperatures are determined by an eikonal equation in Euclidean space. We show that the real-time continuation of these equations implies ballistic propagation. For theories with a free UV fixed point, the ET determines the state at a large modular temperature. In particular, we show that the n→0 limit of Rényi entropies Sn, can be computed from the ET. This establishes a formula for these Rényi entropies for any region in terms of solutions of the eikonal equations. In the n→0 limit, the relevant high-temperature state propagation is determined by a free relativistic Boltzmann equation, with an infinite tower of conserved currents. For the special case of states and regions with a conformal Killing symmetry, these equations coincide with the ones of a perfect fluid.
Fil: Agón, Cesar A.. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
Fil: Casini, Horacio German. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Martinez, Pedro Jorge. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Materia
Information Theory
Unruh Effect
Renyi Entropy
Quantum Field Theory
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/233658
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/233658
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Rényi entropies in the n →0 limit and entanglement temperaturesAgón, Cesar A.Casini, Horacio GermanMartinez, Pedro JorgeInformation TheoryUnruh EffectRenyi EntropyQuantum Field Theoryhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1Entanglement temperatures (ET) are a generalization of Unruh temperatures valid for states reduced to any region of space. They encode in a thermal fashion the high energy behavior of the state around a point. These temperatures are determined by an eikonal equation in Euclidean space. We show that the real-time continuation of these equations implies ballistic propagation. For theories with a free UV fixed point, the ET determines the state at a large modular temperature. In particular, we show that the n→0 limit of Rényi entropies Sn, can be computed from the ET. This establishes a formula for these Rényi entropies for any region in terms of solutions of the eikonal equations. In the n→0 limit, the relevant high-temperature state propagation is determined by a free relativistic Boltzmann equation, with an infinite tower of conserved currents. For the special case of states and regions with a conformal Killing symmetry, these equations coincide with the ones of a perfect fluid.Fil: Agón, Cesar A.. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaFil: Casini, Horacio German. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Martinez, Pedro Jorge. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaAmerican Physical Society2023-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/233658Agón, Cesar A.; Casini, Horacio German; Martinez, Pedro Jorge; Rényi entropies in the n →0 limit and entanglement temperatures; American Physical Society; Physical Review D; 108; 10; 11-2023; 1-232470-00102470-0029CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.aps.org/doi/10.1103/PhysRevD.108.105009info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevD.108.105009info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:11:17Zoai:ri.conicet.gov.ar:11336/233658instacron: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:34982025-10-22 12:11:18.22CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Rényi entropies in the n →0 limit and entanglement temperatures
title Rényi entropies in the n →0 limit and entanglement temperatures
spellingShingle Rényi entropies in the n →0 limit and entanglement temperatures
Agón, Cesar A.
Information Theory
Unruh Effect
Renyi Entropy
Quantum Field Theory
title_short Rényi entropies in the n →0 limit and entanglement temperatures
title_full Rényi entropies in the n →0 limit and entanglement temperatures
title_fullStr Rényi entropies in the n →0 limit and entanglement temperatures
title_full_unstemmed Rényi entropies in the n →0 limit and entanglement temperatures
title_sort Rényi entropies in the n →0 limit and entanglement temperatures
dc.creator.none.fl_str_mv Agón, Cesar A.
Casini, Horacio German
Martinez, Pedro Jorge
author Agón, Cesar A.
author_facet Agón, Cesar A.
Casini, Horacio German
Martinez, Pedro Jorge
author_role author
author2 Casini, Horacio German
Martinez, Pedro Jorge
author2_role author
author
dc.subject.none.fl_str_mv Information Theory
Unruh Effect
Renyi Entropy
Quantum Field Theory
topic Information Theory
Unruh Effect
Renyi Entropy
Quantum Field Theory
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Entanglement temperatures (ET) are a generalization of Unruh temperatures valid for states reduced to any region of space. They encode in a thermal fashion the high energy behavior of the state around a point. These temperatures are determined by an eikonal equation in Euclidean space. We show that the real-time continuation of these equations implies ballistic propagation. For theories with a free UV fixed point, the ET determines the state at a large modular temperature. In particular, we show that the n→0 limit of Rényi entropies Sn, can be computed from the ET. This establishes a formula for these Rényi entropies for any region in terms of solutions of the eikonal equations. In the n→0 limit, the relevant high-temperature state propagation is determined by a free relativistic Boltzmann equation, with an infinite tower of conserved currents. For the special case of states and regions with a conformal Killing symmetry, these equations coincide with the ones of a perfect fluid.
Fil: Agón, Cesar A.. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
Fil: Casini, Horacio German. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Martinez, Pedro Jorge. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
description Entanglement temperatures (ET) are a generalization of Unruh temperatures valid for states reduced to any region of space. They encode in a thermal fashion the high energy behavior of the state around a point. These temperatures are determined by an eikonal equation in Euclidean space. We show that the real-time continuation of these equations implies ballistic propagation. For theories with a free UV fixed point, the ET determines the state at a large modular temperature. In particular, we show that the n→0 limit of Rényi entropies Sn, can be computed from the ET. This establishes a formula for these Rényi entropies for any region in terms of solutions of the eikonal equations. In the n→0 limit, the relevant high-temperature state propagation is determined by a free relativistic Boltzmann equation, with an infinite tower of conserved currents. For the special case of states and regions with a conformal Killing symmetry, these equations coincide with the ones of a perfect fluid.
publishDate 2023
dc.date.none.fl_str_mv 2023-11
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/11336/233658
Agón, Cesar A.; Casini, Horacio German; Martinez, Pedro Jorge; Rényi entropies in the n →0 limit and entanglement temperatures; American Physical Society; Physical Review D; 108; 10; 11-2023; 1-23
2470-0010
2470-0029
CONICET Digital
CONICET
url http://hdl.handle.net/11336/233658
identifier_str_mv Agón, Cesar A.; Casini, Horacio German; Martinez, Pedro Jorge; Rényi entropies in the n →0 limit and entanglement temperatures; American Physical Society; Physical Review D; 108; 10; 11-2023; 1-23
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/url/https://link.aps.org/doi/10.1103/PhysRevD.108.105009
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevD.108.105009
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/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
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score 12.982451

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