Speed Gradient and MaxEnt Principles for Shannon and Tsallis Entropies

Entropy

Alexander L. Fradkov²  Dmitry S. Shalymov¹ 

[1] Mathematics and Mechanics Faculty, Saint-Petersburg State University, Universitetsky prospekt, 28, 198504 Saint-Petersburg, Russia;Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, 61, Bolshoy ave. V.O., 199178 Saint-Petersburg, Russia; E-Mail:

关键词: Shannon entropy;    Tsallis entropy;    maximum entropy (MaxEnt) principle;    non-linear kinetics;    speed-gradient principle;   

DOI  :  10.3390/e17031090

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
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