Random Variables in State Space: Classical Statistical Mechanics of Fluids

Abstract

Using the concepts of probability theory and statistics introduced in Chap. 2, the problem of statistical mechanics can be stated as follows: Consider a system of N particles with momenta and positions p _i , q _i , i = 1, ..., N. At each instant, the microscopic state x = (P ₁, ..., p _N , q _l, ..., q _N ) may be considered as a realization of a random variable in the 6N-dimensional phase space. For this random variable the density function has to be determined under various external, macroscopically given conditions. Furthermore, we will consider only systems in a stationary state so that the density function may be assumed to be time independent.