Entropic Divergence and Entropy Related to Nonlinear Master Equations

We reverse engineer entropy formulas from entropic divergence, optimized to given classes of probability distribution function (PDF) evolution dynamical equation. For linear dynamics of the distribution function, the traditional Kullback–Leibler formula follows from using the logarithm function in t...

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Detalles Bibliográficos
Autores principales: Biró, Tamás Sándor, Néda, Zoltán, Telcs, András
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2019
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514324/
http://dx.doi.org/10.3390/e21100993
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author Biró, Tamás Sándor
Néda, Zoltán
Telcs, András
author_facet Biró, Tamás Sándor
Néda, Zoltán
Telcs, András
author_sort Biró, Tamás Sándor
collection PubMed
description We reverse engineer entropy formulas from entropic divergence, optimized to given classes of probability distribution function (PDF) evolution dynamical equation. For linear dynamics of the distribution function, the traditional Kullback–Leibler formula follows from using the logarithm function in the Csiszár’s f-divergence construction, while for nonlinear master equations more general formulas emerge. As applications, we review a local growth and global reset (LGGR) model for citation distributions, income distribution models and hadron number fluctuations in high energy collisions.
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spelling pubmed-75143242020-11-09 Entropic Divergence and Entropy Related to Nonlinear Master Equations Biró, Tamás Sándor Néda, Zoltán Telcs, András Entropy (Basel) Article We reverse engineer entropy formulas from entropic divergence, optimized to given classes of probability distribution function (PDF) evolution dynamical equation. For linear dynamics of the distribution function, the traditional Kullback–Leibler formula follows from using the logarithm function in the Csiszár’s f-divergence construction, while for nonlinear master equations more general formulas emerge. As applications, we review a local growth and global reset (LGGR) model for citation distributions, income distribution models and hadron number fluctuations in high energy collisions. MDPI 2019-10-11 /pmc/articles/PMC7514324/ http://dx.doi.org/10.3390/e21100993 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
Biró, Tamás Sándor
Néda, Zoltán
Telcs, András
Entropic Divergence and Entropy Related to Nonlinear Master Equations
title Entropic Divergence and Entropy Related to Nonlinear Master Equations
title_full Entropic Divergence and Entropy Related to Nonlinear Master Equations
title_fullStr Entropic Divergence and Entropy Related to Nonlinear Master Equations
title_full_unstemmed Entropic Divergence and Entropy Related to Nonlinear Master Equations
title_short Entropic Divergence and Entropy Related to Nonlinear Master Equations
title_sort entropic divergence and entropy related to nonlinear master equations
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514324/
http://dx.doi.org/10.3390/e21100993
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