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.

现有的大多数非平衡理论都是基于局部平衡假设而开发的，因此在解决远离平衡的动力学过程时会遇到困难。本文中，我们提出了一组动力学方程来描述非平衡二元胶体系统的动力学，该动力学方程是通过将Kramers方程与最大路径信息熵原理相结合而得出的。这些包含局部密度，局部动量和局部动能的方程式相互耦合，最终取决于两体概率分布函数，该函数通过应用最大路径信息熵原理给出了最小偏差的预测。我们表明，所提出的动力学控制方程是自洽的，并可以根据各种局部均衡假设恢复到现有的相关理论。还针对具有几何对称性的几种类型的系统讨论了这些方程式的简化形式。这项工作为研究远离平衡的多组分系统的动力学行为提供了分子水平的理论框架。