Self-consistent equations governing the dynamics of nonequilibrium colloidal systems

Abstract

A self-consistent theoretical procedure is proposed to derive the governing equations for the dynamic properties of nonequilibrium colloidal systems within the framework of the probability theory. Unlike alternative methods in the literature, the self-consistent procedure completely decouples dynamic variables from thermodynamic functions introduced for equilibrium systems. The intrinsic characteristics of a nonequilibrium system is described by the one-body temporal- and spatial-dependent dynamic variables, including the particle density profile, the local momentum, the kinetic energy or dynamic temperature, and by various forms of the two-body position and momentum correlation functions. Within appropriate constraints related to the initial/boundary conditions of a nonequilibrium system, the governing equations for the time evolution of these dynamic functions are obtained by maximizing the information entropy, i.e., the time-evolution equations for the dynamic variables correspond to a probability distribution in the reduced phase space that best represents the known information. It is shown that the dynamic equations are in parallel to and fully consistent with the statistical description of equilibrium systems. With certain assumptions, the self-consistent procedure can be reduced to various conventional theories of nonequilibrium processes.