Dynamics of differential entropy maximization process via the Speed Gradient principle

Abstract

Dynamics of non-stationary processes that follow the MaxEnt principle for differential entropy is considered. A set of equations describing the dynamics of probability density function (pdf) for such processes is proposed. Equations are derived based on the Speed-Gradient principle originated in the control theory. The uniqueness of the limit pdf and asymptotic convergence of pdf are examined under the mass and energy conservation constraints.