Generalizations of Boltzmann's Equation

Abstract

A scheme is proposed for systematically generalizing Boltzmann's equation in order to describe the non-equilibrium behaviour of an arbitrarily dense gas. The method avoids the divergences that arise from considering the dynamics of groups of isolated particles by introducing appropriate damping terms. Transport coefficients are obtained from the kinetic equations by using the autocorrelation formulae. For a one-dimensional gas of impenetrable point particles, approximations to the coefficient of self-diffusion may be obtained readily from the proposed generalization. A first correction to Boltzmann's equation yields the self-diffusion coefficient to within 1 % of its exact value.