Cargando…
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...
Autores principales: | , , |
---|---|
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 |
_version_ | 1783586736168763392 |
---|---|
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]. |
format | Online Article Text |
id | pubmed-7515079 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2019 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
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 |
work_keys_str_mv | AT gomezignacios majorizationanddynamicsofcontinuousdistributions AT dacostabrunog majorizationanddynamicsofcontinuousdistributions AT dossantosmaikeaf majorizationanddynamicsofcontinuousdistributions |