Markoff Random Processes and the Statistical Mechanics of Time-Dependent Phenomena. II. Irreversible Processes in Fluids

TLDR

The study applies previously developed procedures to irreversible processes in fluids. The authors derive phenomenological equations and expressions for viscosity, diffusion, and heat conductivity based on autocorrelation coefficients of phase functions. Using a finite set of plane‑wave expansion coefficients of local particle, momentum, and energy densities as gross variables—chosen with wave numbers small compared to the reciprocal mean interparticle distance—the authors formulate the phenomenological equations. The resulting expressions are valid for both liquids and gases and coincide with Chapman–Enskog predictions for dilute gases.

Abstract

The procedures developed in a previous paper of the same main title are applied to the specific case of irreversible processes in fluids. The gross variables are chosen to be a finite number of the plane-wave expansion coefficients of the local particle, momentum and energy densities. As an example, the gross variables describing the local particle density are ∑ i=1Nexpik·xi,where pi and xi are the momentum and position of the ith molecule and N the total number. k runs over a finite number of values which are all small compared to the reciprocal mean distance between molecules. The phenomenonological equations are derived and expressions are given for the viscosity, diffusion, and heat conductivity in terms the autocorrelation coefficients of certain phase functions. These expressions are supposed to be valid for both liquids and gases. They are shown to coincide with the Chapman-Enskog expressions for dilute gases.