Numerical Experiments on the Stochastic Behavior of a Lennard-Jones Gas System

Abstract

It is known that the hard-sphere gas exhibits strongly stochastic properties. For it, most initially close phase-space-trajectory pairs separate exponentially with time, and Sinai has used this so-called $C$-system behavior to develop a rigorous proof of ergodicity and mixing in the hard-sphere gas. In this paper we numerically integrate the equations of motion for a Lennard-Jones gas, which has attractive as well as repulsive interparticle forces, and we demonstrate that this exponential separation of initially close trajectory pairs persists even in the presence of attractive forces over a fairly wide range of particle densities. In our calculations, this range extends from the dilute-gas region up to densities at which three-body and four-body collisions become significant. Moreover for this density range, we show that an expression for the trajectory-pair rate of exponential separation, rather crudely derived for a hard-sphere gas, fits the empirical Lennard-Jones data quite nicely. Our evidence thus indicates that a gas system with attractive forces can exhibit $C$-system behavior similar to that of the hard-sphere gas. Finally we point out that the exponential separation of trajectories as empirically observed here involves an unusual type of correlated collision sequence.