Legendre transform structure and extremal properties of the relative Fisher information

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 (Schro...

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Autores principales: Venkatesan, R. C., Plastino, Ángel Luis
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2014
Materias:
Física
Relative fisher information
Generalized RFI- Euler theorem
Legendre transform structure
Schrödinger-like link
Inference
Energy eigenvalues
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/101912
https://ri.conicet.gov.ar/11336/23731
https://arxiv.org/abs/1312.4359
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-101912
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Física
Relative fisher information
Generalized RFI- Euler theorem
Legendre transform structure
Schrödinger-like link
Inference
Energy eigenvalues
spellingShingle Física
Relative fisher information
Generalized RFI- Euler theorem
Legendre transform structure
Schrödinger-like link
Inference
Energy eigenvalues
Venkatesan, R. C.
Plastino, Ángel Luis
Legendre transform structure and extremal properties of the relative Fisher information
topic_facet Física
Relative fisher information
Generalized RFI- Euler theorem
Legendre transform structure
Schrödinger-like link
Inference
Energy eigenvalues
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.
format Articulo
Preprint
author Venkatesan, R. C.
Plastino, Ángel Luis
author_facet Venkatesan, R. C.
Plastino, Ángel Luis
author_sort Venkatesan, R. C.
title Legendre transform structure and extremal properties of the relative Fisher information
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
publishDate 2014
url http://sedici.unlp.edu.ar/handle/10915/101912
https://ri.conicet.gov.ar/11336/23731
https://arxiv.org/abs/1312.4359
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AT plastinoangelluis legendretransformstructureandextremalpropertiesoftherelativefisherinformation
bdutipo_str Repositorios
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