Self-Consistent Equations Governing the Dynamics of Non-equilibrium Binary Colloidal Systems

Abstract Most of the existing non-equilibrium theories are developed based on local-equilibrium assumptions and therefore encounter difficulty in addressing dynamical processes far-from-equilibrium. Herein, we present a set of dynamical equations to describe the dynamics of non-equilibrium binary colloidal system, which is derived by combining the Kramers equation with the maximum path information entropy principle. These equations, involving the local density, local momentum and local kinetic energy, are coupled with each other and eventually depend on the two-body probability distribution function, whose least-biased prediction is given by applying the maximum path information entropy principle. We show that the proposed dynamical governing equations are self-consistent, and can recover to the existing relevant theories upon various local equilibrium assumptions. The simplified forms of these equations are also discussed for several types of systems with geometrical symmetries. This work provides a theoretical framework at molecular level for investigating dynamical behaviors of multi-component systems far-from-equilibrium.