Exact Evolution of Reduced Distribution Functions in a Homogeneous Dense Classical Fluid

Abstract

The exact evolution of reduced distribution functions is studied for a homogeneous dense classical fluid by methods which are equivalent to the diagram technique of Prigogine and co-workers. No diagrams or Fourier expansions are used in this work, however. So long as only short-range order is present in the fluid, exact equations for the evolution of the momentum distribution function and for reduced $s$-particle distribution functions are obtained. They are seen to be non-Markovian in a sense explicitly related to the finite duration of a collision. Simple Markovian equations—a generalized master equation for momenta and a functional equation for correlations—result only when the momentum distribution changes negligibly in times of the order of the duration of a collision.