Transport Coefficients from Dissipation in a Canonical Ensemble

Abstract

Expressions for the transport coefficients are obtained by studying the average changes with time which occur in members of a canonical ensemble when the initial state of one particle is partially specified. One calculates, both hydrodynamically and statistical mechanically, an appropriately weighted average of the spread of the initial knowledge. In this way expressions analogous to the Einstein equation for the self-diffusion of a Brownian particle are obtained; viz., the viscosity is proportional to a mean-square center of momentum displacement and the thermal conductivity is related to a mean-square center of energy displacement. These expressions may be converted into the integral of autocorrelation function formulas derived previously by others.