Notions of the ergodic hierarchy for curved statistical manifolds

Autores
Gomez, Ignacio Sebastián
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We present an extension of the ergodic, mixing, and Bernoulli levels of the ergodic hierarchy for statistical models on curved manifolds, making use of elements of the information geometry. This extension focuses on the notion of statistical independence between the microscopical variables of the system. Moreover, we establish an intimately relationship between statistical models and families of probability distributions belonging to the canonical ensemble, which for the case of the quadratic Hamiltonian systems provides a closed form for the correlations between the microvariables in terms of the temperature of the heat bath as a power law. From this, we obtain an information geometric method for studying Hamiltonian dynamics in the canonical ensemble. We illustrate the results with two examples: a pair of interacting harmonic oscillators presenting phase transitions and the 2×2 Gaussian ensembles. In both examples the scalar curvature results a global indicator of the dynamics.
Fil: Gomez, Ignacio Sebastián. 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
2d Correlated Model
Canonical Ensemble
Ergodic Hierarchy
Igeh
Information Geometry
Statistical Models
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/63579
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Notions of the ergodic hierarchy for curved statistical manifoldsGomez, Ignacio Sebastián2d Correlated ModelCanonical EnsembleErgodic HierarchyIgehInformation GeometryStatistical Modelshttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We present an extension of the ergodic, mixing, and Bernoulli levels of the ergodic hierarchy for statistical models on curved manifolds, making use of elements of the information geometry. This extension focuses on the notion of statistical independence between the microscopical variables of the system. Moreover, we establish an intimately relationship between statistical models and families of probability distributions belonging to the canonical ensemble, which for the case of the quadratic Hamiltonian systems provides a closed form for the correlations between the microvariables in terms of the temperature of the heat bath as a power law. From this, we obtain an information geometric method for studying Hamiltonian dynamics in the canonical ensemble. We illustrate the results with two examples: a pair of interacting harmonic oscillators presenting phase transitions and the 2×2 Gaussian ensembles. In both examples the scalar curvature results a global indicator of the dynamics.Fil: Gomez, Ignacio Sebastián. 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; ArgentinaElsevier Science2017-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/63579Gomez, Ignacio Sebastián; Notions of the ergodic hierarchy for curved statistical manifolds; Elsevier Science; Physica A: Statistical Mechanics and its Applications; 484; 10-2017; 117-1310378-4371CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.physa.2017.05.012info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0378437117305149info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:48:16Zoai:ri.conicet.gov.ar:11336/63579instacron: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 09:48:16.325CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Notions of the ergodic hierarchy for curved statistical manifolds
title Notions of the ergodic hierarchy for curved statistical manifolds
spellingShingle Notions of the ergodic hierarchy for curved statistical manifolds
Gomez, Ignacio Sebastián
2d Correlated Model
Canonical Ensemble
Ergodic Hierarchy
Igeh
Information Geometry
Statistical Models
title_short Notions of the ergodic hierarchy for curved statistical manifolds
title_full Notions of the ergodic hierarchy for curved statistical manifolds
title_fullStr Notions of the ergodic hierarchy for curved statistical manifolds
title_full_unstemmed Notions of the ergodic hierarchy for curved statistical manifolds
title_sort Notions of the ergodic hierarchy for curved statistical manifolds
dc.creator.none.fl_str_mv Gomez, Ignacio Sebastián
author Gomez, Ignacio Sebastián
author_facet Gomez, Ignacio Sebastián
author_role author
dc.subject.none.fl_str_mv 2d Correlated Model
Canonical Ensemble
Ergodic Hierarchy
Igeh
Information Geometry
Statistical Models
topic 2d Correlated Model
Canonical Ensemble
Ergodic Hierarchy
Igeh
Information Geometry
Statistical Models
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We present an extension of the ergodic, mixing, and Bernoulli levels of the ergodic hierarchy for statistical models on curved manifolds, making use of elements of the information geometry. This extension focuses on the notion of statistical independence between the microscopical variables of the system. Moreover, we establish an intimately relationship between statistical models and families of probability distributions belonging to the canonical ensemble, which for the case of the quadratic Hamiltonian systems provides a closed form for the correlations between the microvariables in terms of the temperature of the heat bath as a power law. From this, we obtain an information geometric method for studying Hamiltonian dynamics in the canonical ensemble. We illustrate the results with two examples: a pair of interacting harmonic oscillators presenting phase transitions and the 2×2 Gaussian ensembles. In both examples the scalar curvature results a global indicator of the dynamics.
Fil: Gomez, Ignacio Sebastián. 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 We present an extension of the ergodic, mixing, and Bernoulli levels of the ergodic hierarchy for statistical models on curved manifolds, making use of elements of the information geometry. This extension focuses on the notion of statistical independence between the microscopical variables of the system. Moreover, we establish an intimately relationship between statistical models and families of probability distributions belonging to the canonical ensemble, which for the case of the quadratic Hamiltonian systems provides a closed form for the correlations between the microvariables in terms of the temperature of the heat bath as a power law. From this, we obtain an information geometric method for studying Hamiltonian dynamics in the canonical ensemble. We illustrate the results with two examples: a pair of interacting harmonic oscillators presenting phase transitions and the 2×2 Gaussian ensembles. In both examples the scalar curvature results a global indicator of the dynamics.
publishDate 2017
dc.date.none.fl_str_mv 2017-10
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/11336/63579
Gomez, Ignacio Sebastián; Notions of the ergodic hierarchy for curved statistical manifolds; Elsevier Science; Physica A: Statistical Mechanics and its Applications; 484; 10-2017; 117-131
0378-4371
CONICET Digital
CONICET
url http://hdl.handle.net/11336/63579
identifier_str_mv Gomez, Ignacio Sebastián; Notions of the ergodic hierarchy for curved statistical manifolds; Elsevier Science; Physica A: Statistical Mechanics and its Applications; 484; 10-2017; 117-131
0378-4371
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.physa.2017.05.012
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0378437117305149
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
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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