The Friction Coefficient Formalism in the Statistical Mechanics of Transport Processes

Abstract

Kirkwood's theory for the friction coefficient in Brownian motion relates the transport coefficients to the microscopic properties of a system through the time integral of a force autocorrelation function. The expression is useful subject to the validity of certain assumptions on the form of the autocorrelation function. These restrictions and the predicted diffusion coefficients have been examined using the method of molecular dynamics. It is shown that the assumptions are invalid and that when Kirkwood's expression is evaluated exactly it gives negative self-diffusion coefficients. This leads to the conclusion that the friction coefficient approach to transport in simple systems is physically unreasonable and should no longer be used.