Speed Gradient and MaxEnt Principles for Shannon and Tsallis Entropies

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.

Keywords

• Shannon entropy, Tsallis entropy, maximum entropy (MaxEnt) principle, non-linear kinetics, speed-gradient principle