The Shannon entropy as a measure of diffusion in multidimensional dynamical systems

Autores
Giordano, Claudia Marcela; Cincotta, Pablo Miguel
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In the present work, we introduce two new estimators of chaotic diffusion based on the Shannon entropy. Using theoretical, heuristic and numerical arguments, we show that the entropy, S, provides a measure of the diffusion extent of a given small initial ensemble of orbits, while an indicator related with the time derivative of the entropy, S′, estimates the diffusion rate. We show that in the limiting case of near ergodicity, after an appropriate normalization, S′ coincides with the standard homogeneous diffusion coefficient. The very first application of this formulation to a 4D symplectic map and to the Arnold Hamiltonian reveals very successful and encouraging results.
Instituto de Astrofísica de La Plata
Materia
Astronomía
Física
Chaotic diffusion
Multidimensional dynamical systems
Entropy
Rate of diffusion
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/141472
Acceder
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oai_identifier_str oai:sedici.unlp.edu.ar:10915/141472
network_acronym_str SEDICI
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network_name_str SEDICI (UNLP)
spelling The Shannon entropy as a measure of diffusion in multidimensional dynamical systemsGiordano, Claudia MarcelaCincotta, Pablo MiguelAstronomíaFísicaChaotic diffusionMultidimensional dynamical systemsEntropyRate of diffusionIn the present work, we introduce two new estimators of chaotic diffusion based on the Shannon entropy. Using theoretical, heuristic and numerical arguments, we show that the entropy, S, provides a measure of the diffusion extent of a given small initial ensemble of orbits, while an indicator related with the time derivative of the entropy, S′, estimates the diffusion rate. We show that in the limiting case of near ergodicity, after an appropriate normalization, S′ coincides with the standard homogeneous diffusion coefficient. The very first application of this formulation to a 4D symplectic map and to the Arnold Hamiltonian reveals very successful and encouraging results.Instituto de Astrofísica de La Plata2018-04-28info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf1-21http://sedici.unlp.edu.ar/handle/10915/141472enginfo:eu-repo/semantics/altIdentifier/issn/0923-2958info:eu-repo/semantics/altIdentifier/issn/1572-9478info:eu-repo/semantics/altIdentifier/doi/10.1007/s10569-018-9832-xinfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International (CC BY 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-03T11:04:14Zoai:sedici.unlp.edu.ar:10915/141472Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-03 11:04:14.465SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv The Shannon entropy as a measure of diffusion in multidimensional dynamical systems
title The Shannon entropy as a measure of diffusion in multidimensional dynamical systems
spellingShingle The Shannon entropy as a measure of diffusion in multidimensional dynamical systems
Giordano, Claudia Marcela
Astronomía
Física
Chaotic diffusion
Multidimensional dynamical systems
Entropy
Rate of diffusion
title_short The Shannon entropy as a measure of diffusion in multidimensional dynamical systems
title_full The Shannon entropy as a measure of diffusion in multidimensional dynamical systems
title_fullStr The Shannon entropy as a measure of diffusion in multidimensional dynamical systems
title_full_unstemmed The Shannon entropy as a measure of diffusion in multidimensional dynamical systems
title_sort The Shannon entropy as a measure of diffusion in multidimensional dynamical systems
dc.creator.none.fl_str_mv Giordano, Claudia Marcela
Cincotta, Pablo Miguel
author Giordano, Claudia Marcela
author_facet Giordano, Claudia Marcela
Cincotta, Pablo Miguel
author_role author
author2 Cincotta, Pablo Miguel
author2_role author
dc.subject.none.fl_str_mv Astronomía
Física
Chaotic diffusion
Multidimensional dynamical systems
Entropy
Rate of diffusion
topic Astronomía
Física
Chaotic diffusion
Multidimensional dynamical systems
Entropy
Rate of diffusion
dc.description.none.fl_txt_mv In the present work, we introduce two new estimators of chaotic diffusion based on the Shannon entropy. Using theoretical, heuristic and numerical arguments, we show that the entropy, S, provides a measure of the diffusion extent of a given small initial ensemble of orbits, while an indicator related with the time derivative of the entropy, S′, estimates the diffusion rate. We show that in the limiting case of near ergodicity, after an appropriate normalization, S′ coincides with the standard homogeneous diffusion coefficient. The very first application of this formulation to a 4D symplectic map and to the Arnold Hamiltonian reveals very successful and encouraging results.
Instituto de Astrofísica de La Plata
description In the present work, we introduce two new estimators of chaotic diffusion based on the Shannon entropy. Using theoretical, heuristic and numerical arguments, we show that the entropy, S, provides a measure of the diffusion extent of a given small initial ensemble of orbits, while an indicator related with the time derivative of the entropy, S′, estimates the diffusion rate. We show that in the limiting case of near ergodicity, after an appropriate normalization, S′ coincides with the standard homogeneous diffusion coefficient. The very first application of this formulation to a 4D symplectic map and to the Arnold Hamiltonian reveals very successful and encouraging results.
publishDate 2018
dc.date.none.fl_str_mv 2018-04-28
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
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://sedici.unlp.edu.ar/handle/10915/141472
url http://sedici.unlp.edu.ar/handle/10915/141472
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/0923-2958
info:eu-repo/semantics/altIdentifier/issn/1572-9478
info:eu-repo/semantics/altIdentifier/doi/10.1007/s10569-018-9832-x
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
dc.format.none.fl_str_mv application/pdf
1-21
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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score 13.13397

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