A stochastic theory of translational correlation functions in gases and liquids

This paper presents a theory of translational relaxation in hard sphere systems. We construct self-equilibrium time correlation functions for the self-density and for the velocity of a molecule by techniques related to the theory of stochastic point processes. Our stochastic theory yields, at low density, the Boltzmann–Enskog kinetic theory. At intermediate densities we obtain enhancement (t−3/2 decay) and at high density reduction of the velocity autocorrelation function relative to the Boltzmann–Enskog exponential decay in accord with molecular dynamics simulations. The self-diffusion coefficient is correspondingly enhanced and reduced. We also compare our formulation with kinetic theories based on the BBGKY hierarchy. In particular, the relationship of our theory to ring kinetic theory is explored.