Legendre transform structure and extremal properties of the relative Fisher information

Autores
Venkatesan, R. C.; Plastino, Ángel Luis
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Variational extremization of the relative Fisher information (RFI, hereafter) is performed. Reciprocity relations, akin to those of thermodynamics are derived, employing the extremal results of mthe RFI expressed in terms of probability amplitudes. A time independent Schrodinger-like equation (Schrodinger like link) for the RFI is derived. The concomitant Legendre transform structure (LTS hereafter) is developed by utilizing a generalized RFI-Euler theorem, which shows that the entire mathematical structure of htermodynamics translates into the RFI framework, both for equilibrium and non equilibrium cases. The qualitatevily distinct nature of the present results visd-a-vis those of prio studies utilizing the Shannon Entropy and/or the Fisher information mmeasure is discussed. A principled relationship between the RFI and the FIM ferameworks is derived. The utility of this relationship is demosnstrated by an example wherein the energy eigenvalues of the Schroedinger-like link for the RFI are inferred solely using the quantum mechanical virial theorem and the LTS of the RFI.
Fil: Venkatesan, R. C.. Systems Research Corporation; India
Fil: Plastino, Ángel Luis. 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
Relative Fisher Information
Generalized Rfi- Euler Theorem
Legendre Transform Structure
Schrödinger Like Link
Inference
Energy Eigenvalues
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:11336/23731
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/23731
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Legendre transform structure and extremal properties of the relative Fisher informationVenkatesan, R. C.Plastino, Ángel LuisRelative Fisher InformationGeneralized Rfi- Euler TheoremLegendre Transform StructureSchrödinger Like LinkInferenceEnergy Eigenvalueshttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1Variational extremization of the relative Fisher information (RFI, hereafter) is performed. Reciprocity relations, akin to those of thermodynamics are derived, employing the extremal results of mthe RFI expressed in terms of probability amplitudes. A time independent Schrodinger-like equation (Schrodinger like link) for the RFI is derived. The concomitant Legendre transform structure (LTS hereafter) is developed by utilizing a generalized RFI-Euler theorem, which shows that the entire mathematical structure of htermodynamics translates into the RFI framework, both for equilibrium and non equilibrium cases. The qualitatevily distinct nature of the present results visd-a-vis those of prio studies utilizing the Shannon Entropy and/or the Fisher information mmeasure is discussed. A principled relationship between the RFI and the FIM ferameworks is derived. The utility of this relationship is demosnstrated by an example wherein the energy eigenvalues of the Schroedinger-like link for the RFI are inferred solely using the quantum mechanical virial theorem and the LTS of the RFI.Fil: Venkatesan, R. C.. Systems Research Corporation; IndiaFil: Plastino, Ángel Luis. 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; ArgentinaElsevier2014-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/23731Venkatesan, R. C.; Plastino, Ángel Luis; Legendre transform structure and extremal properties of the relative Fisher information; Elsevier; Physics Letters A; 378; 20; 3-2014; 1341-13450375-9601CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0375960114002849info:eu-repo/semantics/altIdentifier/doi/10.1016/j.physleta.2014.03.027info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1312.4359info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-17T10:48:48Zoai:ri.conicet.gov.ar:11336/23731instacron: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:34982025-09-17 10:48:49.111CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Legendre transform structure and extremal properties of the relative Fisher information
title Legendre transform structure and extremal properties of the relative Fisher information
spellingShingle Legendre transform structure and extremal properties of the relative Fisher information
Venkatesan, R. C.
Relative Fisher Information
Generalized Rfi- Euler Theorem
Legendre Transform Structure
Schrödinger Like Link
Inference
Energy Eigenvalues
title_short Legendre transform structure and extremal properties of the relative Fisher information
title_full Legendre transform structure and extremal properties of the relative Fisher information
title_fullStr Legendre transform structure and extremal properties of the relative Fisher information
title_full_unstemmed Legendre transform structure and extremal properties of the relative Fisher information
title_sort Legendre transform structure and extremal properties of the relative Fisher information
dc.creator.none.fl_str_mv Venkatesan, R. C.
Plastino, Ángel Luis
author Venkatesan, R. C.
author_facet Venkatesan, R. C.
Plastino, Ángel Luis
author_role author
author2 Plastino, Ángel Luis
author2_role author
dc.subject.none.fl_str_mv Relative Fisher Information
Generalized Rfi- Euler Theorem
Legendre Transform Structure
Schrödinger Like Link
Inference
Energy Eigenvalues
topic Relative Fisher Information
Generalized Rfi- Euler Theorem
Legendre Transform Structure
Schrödinger Like Link
Inference
Energy Eigenvalues
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Variational extremization of the relative Fisher information (RFI, hereafter) is performed. Reciprocity relations, akin to those of thermodynamics are derived, employing the extremal results of mthe RFI expressed in terms of probability amplitudes. A time independent Schrodinger-like equation (Schrodinger like link) for the RFI is derived. The concomitant Legendre transform structure (LTS hereafter) is developed by utilizing a generalized RFI-Euler theorem, which shows that the entire mathematical structure of htermodynamics translates into the RFI framework, both for equilibrium and non equilibrium cases. The qualitatevily distinct nature of the present results visd-a-vis those of prio studies utilizing the Shannon Entropy and/or the Fisher information mmeasure is discussed. A principled relationship between the RFI and the FIM ferameworks is derived. The utility of this relationship is demosnstrated by an example wherein the energy eigenvalues of the Schroedinger-like link for the RFI are inferred solely using the quantum mechanical virial theorem and the LTS of the RFI.
Fil: Venkatesan, R. C.. Systems Research Corporation; India
Fil: Plastino, Ángel Luis. 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 Variational extremization of the relative Fisher information (RFI, hereafter) is performed. Reciprocity relations, akin to those of thermodynamics are derived, employing the extremal results of mthe RFI expressed in terms of probability amplitudes. A time independent Schrodinger-like equation (Schrodinger like link) for the RFI is derived. The concomitant Legendre transform structure (LTS hereafter) is developed by utilizing a generalized RFI-Euler theorem, which shows that the entire mathematical structure of htermodynamics translates into the RFI framework, both for equilibrium and non equilibrium cases. The qualitatevily distinct nature of the present results visd-a-vis those of prio studies utilizing the Shannon Entropy and/or the Fisher information mmeasure is discussed. A principled relationship between the RFI and the FIM ferameworks is derived. The utility of this relationship is demosnstrated by an example wherein the energy eigenvalues of the Schroedinger-like link for the RFI are inferred solely using the quantum mechanical virial theorem and the LTS of the RFI.
publishDate 2014
dc.date.none.fl_str_mv 2014-03
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/11336/23731
Venkatesan, R. C.; Plastino, Ángel Luis; Legendre transform structure and extremal properties of the relative Fisher information; Elsevier; Physics Letters A; 378; 20; 3-2014; 1341-1345
0375-9601
CONICET Digital
CONICET
url http://hdl.handle.net/11336/23731
identifier_str_mv Venkatesan, R. C.; Plastino, Ángel Luis; Legendre transform structure and extremal properties of the relative Fisher information; Elsevier; Physics Letters A; 378; 20; 3-2014; 1341-1345
0375-9601
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0375960114002849
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.physleta.2014.03.027
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1312.4359
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
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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 13.001348

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