Order and disorder in the approach to equilibrium of a classical gas

We study the approach to equilibrium of a classical gas. The initial condition corresponds to a Maxwell velocity distribution, but to a nonequilibrium binary correlation. We consider two cases. In the first, there are initially no spatial correlations, while in the second, initial correlations correspond to long-range spatial order. We show that the gas leaves the Maxwell velocity distribution function in the process of building up equilibrium correlations. The spatial correlations in the equilibrium state are seen to emerge from a self-organization process in the gas. Non-Markovian effects play an essential role in this process by coupling the velocity distribution and the binary correlations. For the case of initial long-range correlations we obtain anti-Boltzmann behavior in the evolution of the velocity distribution as the Boltzmann entropy decreases from the nonequilibrium to the equilibrium state. For this case we also have nontrivial behavior on a short time scale due to the non-Markovian effects. The approach used here is based on the theory of subdynamics as developed in previous publications. The results obtained show the interplay between irreversible processes leading to disorder and to order in a classical gas.