Department of Chemical and Environmental Engineering, University of California, Riverside, California 92521, USA.
J Chem Phys. 2011 Feb 7;134(5):054514. doi: 10.1063/1.3537972.
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.
提出了一种自洽的理论方法，用于从概率论的框架中推导出非平衡胶体系统动力学性质的控制方程。与文献中的其他方法不同，自洽方法完全将动力学变量与为平衡系统引入的热力学函数解耦。非平衡系统的固有特性由单粒子随时间和空间变化的动力学变量来描述，包括粒子密度分布、局部动量、动能或动态温度，以及各种形式的双粒子位置和动量相关函数。在与非平衡系统的初始/边界条件相关的适当约束下，通过最大化信息熵来获得这些动力学函数的时间演化的控制方程，即，动力学变量的时间演化方程对应于在约化相空间中最佳表示已知信息的概率分布。结果表明，动力学方程与平衡系统的统计描述是并行的，并且完全一致。在某些假设下，自洽方法可以简化为各种非平衡过程的常规理论。
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