Shannon entropy diffusion estimates: sensitivity on the parameters of the method

Autores
Cincotta, Pablo Miguel; Giordano, Claudia Marcela; Alves Silva, Raphael; Beaugé, Cristián
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In the present effort, we revisit the Shannon entropy approach for the study of both the extent and the rate of diffusion in a given dynamical system. In particular, we provide a theoretical and numerical study of the dependence of the formulation on the parameters of the method. We succeed in deriving not only a diffusion coefficient, DS, but also an estimate of the macroscopical instability time for the system under study. Dealing with a toy model, namely a 4D symplectic application that represents the dynamics around a junction of resonances of different order, and an a particular case of the planar three-body problem, the HD20003 planetary system, we obtain numerical evidence that DS is a robust measure of the diffusion rate, no significant dependence on the free parameter of the entropy formulation (the size of the elements of the partition) being observed. Moreover, successful results concerning the estimation of macroscopical instability times obtained from DS are presented in both cases.
Facultad de Ciencias Astronómicas y Geofísicas
Instituto de Astrofísica de La Plata
Materia
Astronomía
Chaotic diffusion
Resonances
Shannon entropy
Three-body problem
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:10915/145267
Acceder
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network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling Shannon entropy diffusion estimates: sensitivity on the parameters of the methodCincotta, Pablo MiguelGiordano, Claudia MarcelaAlves Silva, RaphaelBeaugé, CristiánAstronomíaChaotic diffusionResonancesShannon entropyThree-body problemIn the present effort, we revisit the Shannon entropy approach for the study of both the extent and the rate of diffusion in a given dynamical system. In particular, we provide a theoretical and numerical study of the dependence of the formulation on the parameters of the method. We succeed in deriving not only a diffusion coefficient, D<sub>S</sub>, but also an estimate of the macroscopical instability time for the system under study. Dealing with a toy model, namely a 4D symplectic application that represents the dynamics around a junction of resonances of different order, and an a particular case of the planar three-body problem, the HD20003 planetary system, we obtain numerical evidence that D<sub>S</sub> is a robust measure of the diffusion rate, no significant dependence on the free parameter of the entropy formulation (the size of the elements of the partition) being observed. Moreover, successful results concerning the estimation of macroscopical instability times obtained from D<sub>S</sub> are presented in both cases.Facultad de Ciencias Astronómicas y GeofísicasInstituto de Astrofísica de La Plata2021-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://sedici.unlp.edu.ar/handle/10915/145267enginfo:eu-repo/semantics/altIdentifier/issn/0923-2958info:eu-repo/semantics/altIdentifier/issn/1572-9478info:eu-repo/semantics/altIdentifier/doi/10.1007/s10569-021-10006-yinfo: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:UNLP2025-09-29T11:32:16Zoai:sedici.unlp.edu.ar:10915/145267Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:32:17.253SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Shannon entropy diffusion estimates: sensitivity on the parameters of the method
title Shannon entropy diffusion estimates: sensitivity on the parameters of the method
spellingShingle Shannon entropy diffusion estimates: sensitivity on the parameters of the method
Cincotta, Pablo Miguel
Astronomía
Chaotic diffusion
Resonances
Shannon entropy
Three-body problem
title_short Shannon entropy diffusion estimates: sensitivity on the parameters of the method
title_full Shannon entropy diffusion estimates: sensitivity on the parameters of the method
title_fullStr Shannon entropy diffusion estimates: sensitivity on the parameters of the method
title_full_unstemmed Shannon entropy diffusion estimates: sensitivity on the parameters of the method
title_sort Shannon entropy diffusion estimates: sensitivity on the parameters of the method
dc.creator.none.fl_str_mv Cincotta, Pablo Miguel
Giordano, Claudia Marcela
Alves Silva, Raphael
Beaugé, Cristián
author Cincotta, Pablo Miguel
author_facet Cincotta, Pablo Miguel
Giordano, Claudia Marcela
Alves Silva, Raphael
Beaugé, Cristián
author_role author
author2 Giordano, Claudia Marcela
Alves Silva, Raphael
Beaugé, Cristián
author2_role author
author
author
dc.subject.none.fl_str_mv Astronomía
Chaotic diffusion
Resonances
Shannon entropy
Three-body problem
topic Astronomía
Chaotic diffusion
Resonances
Shannon entropy
Three-body problem
dc.description.none.fl_txt_mv In the present effort, we revisit the Shannon entropy approach for the study of both the extent and the rate of diffusion in a given dynamical system. In particular, we provide a theoretical and numerical study of the dependence of the formulation on the parameters of the method. We succeed in deriving not only a diffusion coefficient, D<sub>S</sub>, but also an estimate of the macroscopical instability time for the system under study. Dealing with a toy model, namely a 4D symplectic application that represents the dynamics around a junction of resonances of different order, and an a particular case of the planar three-body problem, the HD20003 planetary system, we obtain numerical evidence that D<sub>S</sub> is a robust measure of the diffusion rate, no significant dependence on the free parameter of the entropy formulation (the size of the elements of the partition) being observed. Moreover, successful results concerning the estimation of macroscopical instability times obtained from D<sub>S</sub> are presented in both cases.
Facultad de Ciencias Astronómicas y Geofísicas
Instituto de Astrofísica de La Plata
description In the present effort, we revisit the Shannon entropy approach for the study of both the extent and the rate of diffusion in a given dynamical system. In particular, we provide a theoretical and numerical study of the dependence of the formulation on the parameters of the method. We succeed in deriving not only a diffusion coefficient, D<sub>S</sub>, but also an estimate of the macroscopical instability time for the system under study. Dealing with a toy model, namely a 4D symplectic application that represents the dynamics around a junction of resonances of different order, and an a particular case of the planar three-body problem, the HD20003 planetary system, we obtain numerical evidence that D<sub>S</sub> is a robust measure of the diffusion rate, no significant dependence on the free parameter of the entropy formulation (the size of the elements of the partition) being observed. Moreover, successful results concerning the estimation of macroscopical instability times obtained from D<sub>S</sub> are presented in both cases.
publishDate 2021
dc.date.none.fl_str_mv 2021-02
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/10915/145267
url http://sedici.unlp.edu.ar/handle/10915/145267
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/s10569-021-10006-y
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
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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