Evolution of Reduced Distribution Functions for Inhomogeneous Dense Classical Fluids

Abstract

The evolution of reduced distribution functions is studied for an inhomogeneous dense classical fluid by methods previously used to study homogeneous fluids. So long as only short-range order is present in the fluid and the variation in properties caused by the inhomogeneity is negligible over distances of the order of the region of a collision, then the evolution equations for the one-particle and $s$-particle distribution functions are obtained. They take a simple Markovian form if the one-particle distribution changes negligibly in times of the order of the duration of a collision. The operators involved in the evolution equations are studied. Their physical meaning and relationship to the classical Boltzmann equation are considered.