Exact Analysis of a Spatially Nonequilibrium Knudsen Gas

Abstract

The exact irreversible behavior of a gas of noninteracting particles bouncing elastically from the walls of a rectangular box is studied. The gas is spatially inhomogeneous at the beginning. The results indicate that a dynamic equation invariant under time inversion can give an irreversible solution. The general solution has been applied to the specific example of free expansion. Closed form analytic expressions for the evolution of the distributions of position, momentum, and temperature and for the change of entropy have been obtained. Based on the results of this problem, a more general view of the origin of irreversibility is presented.