  Thermalization of classical fields is investigated in a \phi^4 scalar field
theory in 1+1 dimensions, discretized on a lattice. We numerically integrate
the classical equations of motion using initial conditions sampled from various
nonequilibrium probability distributions. Time-dependent expectation values of
observables constructed from the canonical momentum are compared with thermal
ones. It is found that a closed system, evolving from one initial condition,
thermalizes to high precision in the thermodynamic limit, in a time-averaged
sense. For ensembles consisting of many members with the same energy, we find
that expectation values become stationary - and equal to the thermal values -
in the limit of infinitely many members. Initial ensembles with a nonzero
(noncanonical) spread in the energy density or other conserved quantities
evolve to noncanonical stationary ensembles. In the case of a narrow spread,
asymptotic values of primary observables are only mildly affected. In contrast,
fluctuations and connected correlation functions will differ substantially from
the canonical values. This raises doubts on the use of a straightforward
expansion in terms of 1PI-vertex functions to study thermalization.
