The maximum entropy principle for non-equilibrium phase transitions: Determination of order parameters, slaved modes, and emerging patterns

Abstract

The maximum entropy principle allows one to make guesses on the distribution function of systems by maximizing the information entropy under given constraints. In a previous paper we succeeded to formulate appropriate constraints for systems undergoing nonequilibrium phase transitions, but we had to confine our treatment to the order parameters. In this paper we describe a formalism which does not require any a priori knowledge on the order parameters but rather allows us to determine these as well as the slaved modes and the emerging patterns. The method is applicable also to non-physical systems such as neural nets. Our approach allows us to reconsider the Landau theory of phase transitions from a new point of view. A guess is made on the Fokker-Planck equation underlying the processes which give rise to stationary distribution functions of a single order parameter.