Autocorrelation functions in the generalized Boltzmann-Enskog model

The purpose of this paper is to study the asymptotic properties of time autocorrelation functions for the generalized nonlinear Boltzmann-Enskog model, which contains a long-range component of the interaction between the particles. On the basis of the analysis of non-linear features of the Boltzmann-Enskog kinetic equation, the role of nonlinear effects is directly revealed at the approach to an equilibrium state. It is shown that autocorrelation functions have power asymptotics $t^{-3/2}$, and the effects that are related to the inclusion of the long-range component lead to a change in the coefficient at $t^{-3/2}$. These results establish a closed expression for the determination of coefficients in the asymptotic expansion of the autocorrelation functions of rate and thermal diffusion.