  We investigate the time evolution of a classical ensemble of isolated
periodic chains of O(N)-symmetric anharmonic oscillators. Our method is based
on an exact evolution equation for the time dependence of correlation
functions. We discuss its solutions in an approximation which retains all
contributions in next-to-leading order in a 1/N expansion and preserves time
reflection symmetry. We observe effective irreversibility and approximate
thermalization. At large time the system approaches stationary solutions in the
vicinity of, but not identical to, thermal equilibrium. The ensemble therefore
retains some memory of the initial condition beyond the conserved total energy.
Such a behavior with incomplete thermalization is referred to as "mesoscopic
dynamics". It is expected for systems in a small volume. Surprisingly, we find
that the nonthermal asymptotic stationary solutions do not change for large
volume. This raises questions on Boltzmann's conjecture that macroscopic
isolated systems thermalize.
