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

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.