  We study the approach to equilibrium for a scalar field which is coupled to a
large thermal bath. Our analysis of the initial value problem is based on
Kadanoff-Baym equations which are shown to be equivalent to a stochastic
Langevin equation. The interaction with the thermal bath generates a
temperature-dependent spectral density, either through decay and inverse decay
processes or via Landau damping. In equilibrium, energy density and pressure
are determined by the Bose-Einstein distribution function evaluated at a
complex quasi-particle pole. The time evolution of the statistical propagator
is compared with solutions of the Boltzmann equations for particles as well as
quasi-particles. The dependence on initial conditions and the range of validity
of the Boltzmann approximation are determined.
