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Majorization and Dynamics of Continuous Distributions

Instituto de Física, Universidade Federal da Bahia, Rua Barao de Jeremoabo, Salvador–BA 40170-115, Brazil
Instituto Federal de Educação, Ciência e Tecnologia do Sertão Pernambucano, BR 407, km 08, Petrolina 56314-520, Pernambuco, Brazil
Centro Brasileiro de Pesquisas Físicas, Caixa Postal 15051, Rio de Janeiro CEP 91501-970, RJ, Brazil
Author to whom correspondence should be addressed.
Entropy 2019, 21(6), 590;
Received: 17 May 2019 / Revised: 10 June 2019 / Accepted: 12 June 2019 / Published: 14 June 2019
(This article belongs to the Special Issue Quantum Chaos and Complexity)
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 ϕ 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 ϕ ( x ) = x ln x . View Full-Text
Keywords: continuous majorization; ordered chain; convex functions; H-theorem continuous majorization; ordered chain; convex functions; H-theorem
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Gomez, I.S.; da Costa, B.G.; dos Santos, M.A.F. Majorization and Dynamics of Continuous Distributions. Entropy 2019, 21, 590.

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