Evolution Laws for Non-Stationary Processes that Follow the MaxEnt Principle

A. L. Fradkov^ab, D. S. Shalymov<sup>b

a</sup> Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg
^b Saint Petersburg State University

Abstract: In this paper a new justi_cation of maximum entropy production principle (MEPP) is proposed. The dynamics of systems with continuous distribution of parameters are reviewed on the basis of the extreme principle of the speed gradient and on the condition that the system follows the principle of maximum entropy. A set of equations is derived to describe the dynamics of the probability distribution function (pdf). It is shown that for pdfs with compact carrier the limit pdf is unique and can be obtained from Jaynes's MaxEnt principle. The asymptotic convergence is proved. The constraints imposed are the mass conservation law and the energy conservation law.

Keywords: MaxEnt, MEPP, Speed Gradient Principle, Gibbs Distribution.

UDC: 519.722, 536.758