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Majorization and Dynamics of Continuous Distributions

In this work we show how the concept of majorization in continuous distributions can be employed to characterize mixing, diffusive, and quantum dynamics along with the H-Boltzmann theorem. The key point lies in that the definition of majorization allows choosing a wide range of convex functions [For...

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Detalles Bibliográficos
Autores principales: Gomez, Ignacio S., da Costa, Bruno G., dos Santos, Maike A. F.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2019
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7515079/
https://www.ncbi.nlm.nih.gov/pubmed/33267304
http://dx.doi.org/10.3390/e21060590
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author Gomez, Ignacio S.
da Costa, Bruno G.
dos Santos, Maike A. F.
author_facet Gomez, Ignacio S.
da Costa, Bruno G.
dos Santos, Maike A. F.
author_sort Gomez, Ignacio S.
collection PubMed
description In this work we show how the concept of majorization in continuous distributions can be employed to characterize mixing, diffusive, and quantum dynamics along with the H-Boltzmann theorem. The key point lies in that the definition of majorization allows choosing a wide range of convex functions [Formula: see text] for studying a given dynamics. By choosing appropriate convex functions, mixing dynamics, generalized Fokker–Planck equations, and quantum evolutions are characterized as majorized ordered chains along the time evolution, being the stationary states the infimum elements. Moreover, assuming a dynamics satisfying continuous majorization, the H-Boltzmann theorem is obtained as a special case for [Formula: see text].
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spelling pubmed-75150792020-11-09 Majorization and Dynamics of Continuous Distributions Gomez, Ignacio S. da Costa, Bruno G. dos Santos, Maike A. F. Entropy (Basel) Article In this work we show how the concept of majorization in continuous distributions can be employed to characterize mixing, diffusive, and quantum dynamics along with the H-Boltzmann theorem. The key point lies in that the definition of majorization allows choosing a wide range of convex functions [Formula: see text] for studying a given dynamics. By choosing appropriate convex functions, mixing dynamics, generalized Fokker–Planck equations, and quantum evolutions are characterized as majorized ordered chains along the time evolution, being the stationary states the infimum elements. Moreover, assuming a dynamics satisfying continuous majorization, the H-Boltzmann theorem is obtained as a special case for [Formula: see text]. MDPI 2019-06-14 /pmc/articles/PMC7515079/ /pubmed/33267304 http://dx.doi.org/10.3390/e21060590 Text en © 2019 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
Gomez, Ignacio S.
da Costa, Bruno G.
dos Santos, Maike A. F.
Majorization and Dynamics of Continuous Distributions
title Majorization and Dynamics of Continuous Distributions
title_full Majorization and Dynamics of Continuous Distributions
title_fullStr Majorization and Dynamics of Continuous Distributions
title_full_unstemmed Majorization and Dynamics of Continuous Distributions
title_short Majorization and Dynamics of Continuous Distributions
title_sort majorization and dynamics of continuous distributions
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7515079/
https://www.ncbi.nlm.nih.gov/pubmed/33267304
http://dx.doi.org/10.3390/e21060590
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