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Entropy 2015, 17(3), 1090-1102; doi:10.3390/e17031090

Speed Gradient and MaxEnt Principles for Shannon and Tsallis Entropies

1
Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, 61, Bolshoy ave. V.O., 199178 Saint-Petersburg, Russia
2
Mathematics and Mechanics Faculty, Saint-Petersburg State University, Universitetsky prospekt, 28, 198504 Saint-Petersburg, Russia
*
Author to whom correspondence should be addressed.
Academic Editor: Giorgio Kaniadakis
Received: 22 December 2014 / Revised: 25 February 2015 / Accepted: 2 March 2015 / Published: 6 March 2015
(This article belongs to the Special Issue Entropic Aspects in Statistical Physics of Complex Systems)
View Full-Text   |   Download PDF [241 KB, uploaded 6 March 2015]

Abstract

In this paper we consider dynamics of non-stationary processes that follow the MaxEnt principle. We derive a set of equations describing dynamics of a system for Shannon and Tsallis entropies. Systems with discrete probability distribution are considered under mass conservation and energy conservation constraints. The existence and uniqueness of solution are established and asymptotic stability of the equilibrium is proved. Equations are derived based on the speed-gradient principle originated in control theory. View Full-Text
Keywords: Shannon entropy, Tsallis entropy, maximum entropy (MaxEnt) principle, non-linear kinetics, speed-gradient principle Shannon entropy, Tsallis entropy, maximum entropy (MaxEnt) principle, non-linear kinetics, speed-gradient principle
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Fradkov, A.L.; Shalymov, D.S. Speed Gradient and MaxEnt Principles for Shannon and Tsallis Entropies. Entropy 2015, 17, 1090-1102.

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