Cargando…

Useful Dual Functional of Entropic Information Measures

There are entropic functionals galore, but not simple objective measures to distinguish between them. We remedy this situation here by appeal to Born’s proposal, of almost a hundred years ago, that the square modulus of any wave function [Formula: see text] be regarded as a probability distribution...

Descripción completa

Detalles Bibliográficos
Autores principales: Plastino, Angelo, Rocca, Mario Carlos, Pennini, Flavia
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7516974/
https://www.ncbi.nlm.nih.gov/pubmed/33286262
http://dx.doi.org/10.3390/e22040491
_version_ 1783587121850744832
author Plastino, Angelo
Rocca, Mario Carlos
Pennini, Flavia
author_facet Plastino, Angelo
Rocca, Mario Carlos
Pennini, Flavia
author_sort Plastino, Angelo
collection PubMed
description There are entropic functionals galore, but not simple objective measures to distinguish between them. We remedy this situation here by appeal to Born’s proposal, of almost a hundred years ago, that the square modulus of any wave function [Formula: see text] be regarded as a probability distribution P. the usefulness of using information measures like Shannon’s in this pure-state context has been highlighted in [Phys. Lett. A1993, 181, 446]. Here we will apply the notion with the purpose of generating a dual functional [[Formula: see text]], which maps entropic functionals onto positive real numbers. In such an endeavor, we use as standard ingredients the coherent states of the harmonic oscillator (CHO), which are unique in the sense of possessing minimum uncertainty. This use is greatly facilitated by the fact that the CHO can be given analytic, compact closed form as shown in [Rev. Mex. Fis. E 2019, 65, 191]. Rewarding insights are to be obtained regarding the comparison between several standard entropic measures.
format Online
Article
Text
id pubmed-7516974
institution National Center for Biotechnology Information
language English
publishDate 2020
publisher MDPI
record_format MEDLINE/PubMed
spelling pubmed-75169742020-11-09 Useful Dual Functional of Entropic Information Measures Plastino, Angelo Rocca, Mario Carlos Pennini, Flavia Entropy (Basel) Article There are entropic functionals galore, but not simple objective measures to distinguish between them. We remedy this situation here by appeal to Born’s proposal, of almost a hundred years ago, that the square modulus of any wave function [Formula: see text] be regarded as a probability distribution P. the usefulness of using information measures like Shannon’s in this pure-state context has been highlighted in [Phys. Lett. A1993, 181, 446]. Here we will apply the notion with the purpose of generating a dual functional [[Formula: see text]], which maps entropic functionals onto positive real numbers. In such an endeavor, we use as standard ingredients the coherent states of the harmonic oscillator (CHO), which are unique in the sense of possessing minimum uncertainty. This use is greatly facilitated by the fact that the CHO can be given analytic, compact closed form as shown in [Rev. Mex. Fis. E 2019, 65, 191]. Rewarding insights are to be obtained regarding the comparison between several standard entropic measures. MDPI 2020-04-24 /pmc/articles/PMC7516974/ /pubmed/33286262 http://dx.doi.org/10.3390/e22040491 Text en © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Plastino, Angelo
Rocca, Mario Carlos
Pennini, Flavia
Useful Dual Functional of Entropic Information Measures
title Useful Dual Functional of Entropic Information Measures
title_full Useful Dual Functional of Entropic Information Measures
title_fullStr Useful Dual Functional of Entropic Information Measures
title_full_unstemmed Useful Dual Functional of Entropic Information Measures
title_short Useful Dual Functional of Entropic Information Measures
title_sort useful dual functional of entropic information measures
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7516974/
https://www.ncbi.nlm.nih.gov/pubmed/33286262
http://dx.doi.org/10.3390/e22040491
work_keys_str_mv AT plastinoangelo usefuldualfunctionalofentropicinformationmeasures
AT roccamariocarlos usefuldualfunctionalofentropicinformationmeasures
AT penniniflavia usefuldualfunctionalofentropicinformationmeasures