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 <i>H</i>-Boltzmann theorem. The key point lies in that the definition of majorization allows choosing a wide range of co...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-06-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/21/6/590 |
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| author | Ignacio S. Gomez Bruno G. da Costa Maike A. F. dos Santos |
| author_facet | Ignacio S. Gomez Bruno G. da Costa Maike A. F. dos Santos |
| author_sort | Ignacio S. Gomez |
| collection | DOAJ |
| 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 <i>H</i>-Boltzmann theorem. The key point lies in that the definition of majorization allows choosing a wide range of convex functions <inline-formula> <math display="inline"> <semantics> <mi>ϕ</mi> </semantics> </math> </inline-formula> 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 <i>H</i>-Boltzmann theorem is obtained as a special case for <inline-formula> <math display="inline"> <semantics> <mrow> <mi>ϕ</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>=</mo> <mi>x</mi> <mo form="prefix">ln</mo> <mi>x</mi> </mrow> </semantics> </math> </inline-formula>. |
| first_indexed | 2024-04-11T18:23:23Z |
| format | Article |
| id | doaj.art-991284b2044e4514a33306d38713ac62 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T18:23:23Z |
| publishDate | 2019-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-991284b2044e4514a33306d38713ac622022-12-22T04:09:43ZengMDPI AGEntropy1099-43002019-06-0121659010.3390/e21060590e21060590Majorization and Dynamics of Continuous DistributionsIgnacio S. Gomez0Bruno G. da Costa1Maike A. F. dos Santos2Instituto de Física, Universidade Federal da Bahia, Rua Barao de Jeremoabo, Salvador–BA 40170-115, BrazilInstituto Federal de Educação, Ciência e Tecnologia do Sertão Pernambucano, BR 407, km 08, Petrolina 56314-520, Pernambuco, BrazilCentro Brasileiro de Pesquisas Físicas, Caixa Postal 15051, Rio de Janeiro CEP 91501-970, RJ, BrazilIn 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 <i>H</i>-Boltzmann theorem. The key point lies in that the definition of majorization allows choosing a wide range of convex functions <inline-formula> <math display="inline"> <semantics> <mi>ϕ</mi> </semantics> </math> </inline-formula> 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 <i>H</i>-Boltzmann theorem is obtained as a special case for <inline-formula> <math display="inline"> <semantics> <mrow> <mi>ϕ</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>=</mo> <mi>x</mi> <mo form="prefix">ln</mo> <mi>x</mi> </mrow> </semantics> </math> </inline-formula>.https://www.mdpi.com/1099-4300/21/6/590continuous majorizationordered chainconvex functions<i>H</i>-theorem |
| spellingShingle | Ignacio S. Gomez Bruno G. da Costa Maike A. F. dos Santos Majorization and Dynamics of Continuous Distributions Entropy continuous majorization ordered chain convex functions <i>H</i>-theorem |
| 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 | continuous majorization ordered chain convex functions <i>H</i>-theorem |
| url | https://www.mdpi.com/1099-4300/21/6/590 |
| work_keys_str_mv | AT ignaciosgomez majorizationanddynamicsofcontinuousdistributions AT brunogdacosta majorizationanddynamicsofcontinuousdistributions AT maikeafdossantos majorizationanddynamicsofcontinuousdistributions |