On the time evolution of large systems. A soluble model

Abstract

We study the time evolution of a large system consisting of two kinds of particles that can be transformed into each other by an external field. Hydrodynamic equations are derived. The approach to equilibrium of densities and correlation functions is oscillatory with a slowly decaying amplitude like t^{−$\text{1}\text{2}$} for large times t. Generalized $\text{H}$ theorems hold, but for large t the $\text{H}$ quantity again oscillates around the new equilibrium value. Possible removal of these oscillations by coarse-graining is discussed.