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Open AccessArticle

Entropic Divergence and Entropy Related to Nonlinear Master Equations

by Tamás Sándor Biró 1,*,†,‡, Zoltán Néda 2 and András Telcs 1,3,4,5
Wigner Research Centre for Physics, 1121 Budapest, Hungary
Department of Physics, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania
Department of Computer Science and Information Theory, Budapest University of Technology and Economics, 1111 Budapest, Hungary
Department of Quantitative Methods, University of Pannonia, 8200 Veszprém, Hungary
VIAS Virtual Institute for Advanced Studies, 1039 Budapest, Hungary
Author to whom correspondence should be addressed.
Based on a talk given at JETC, Barcelona, 21–24 May 2019.
External faculty, Complex Science Hub, 1080 Vienna, Austria.
Entropy 2019, 21(10), 993;
Received: 11 September 2019 / Revised: 2 October 2019 / Accepted: 8 October 2019 / Published: 11 October 2019
(This article belongs to the Special Issue Selected Papers from 15th Joint European Thermodynamics Conference)
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. View Full-Text
Keywords: entropy; entropic divergence; master equation; reset; preferential growth entropy; entropic divergence; master equation; reset; preferential growth
MDPI and ACS Style

Biró, T.S.; Néda, Z.; Telcs, A. Entropic Divergence and Entropy Related to Nonlinear Master Equations. Entropy 2019, 21, 993.

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