A
Theoretical Study of Dynamic Governing Equations for Binary Colloidal Systems
Combined BBGKY Hierarchy and Maximum Path Information Entropy Principle

Teng Zhao[1],
Shuangliang Zhao^{1, 1} and Honglai Liu^{2, *}

¹ State Key
laboratory of Chemical Engineering and School of Chemical Engineering, East
China University of Science and Technology, Shanghai, 200237, China

² School of
Chemistry and Molecular Engineering, East China University of Science and
Technology, Shanghai, 200237, China

Abstract

Most of the
existing non-equilibrium theories based on the local-equilibrium assumption
have difficulty in applying to far-from-equilibrium conditions. Herein, we
conduct a theoretical research on non-equilibrium systems that composed of
binary colloidal mixtures with a combination of Bogoliubove-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy equation and Maximum Path
Information Entropy principle. A set of coupled dynamical governing equations
derived from the first BBGKY correlation function. The dynamic variables that
characterize hydrodynamic properties of the system include local density
profile, local momentum and local kinetic energy abided by the key thoughts of macro-reproducibility. After that, we apply
principle of Maximum Path Information Entropy to give the least-biased
estimation for probability distribution function subject to dynamic constraints
and normalization condition. It is noteworthy that all dynamic variables are
naturally path-dependent. With the
help of this statistical inference method, it is provable that the correlative
time evolution equations are self-consistent. Moreover, the dynamic equation is
consistent with that in the continuous limit with appropriate assumptions. This
work provides a new theoretical computational method for dealing with
non-equilibrium transportation phenomena.

Keywords: Non-equilibrium;
BBGKY hierarchy; Maximum Path Information Entropy principle; Dynamical
governing equations; Self-consistent