  Nonperturbative dynamics of quantum fields out of equilibrium is often
described by the time evolution of a hierarchy of correlation functions, using
approximation methods such as Hartree, large N, and nPI-effective action
techniques. These truncation schemes can be implemented equally well in a
classical statistical system, where results can be tested by comparison with
the complete nonlinear evolution obtained by numerical methods. For a 1+1
dimensional scalar field we find that the early-time behaviour is reproduced
qualitatively by the Hartree dynamics. The inclusion of direct scattering
improves this to the quantitative level. We show that the emergence of
nonthermal temperature profiles at intermediate times can be understood in
terms of the fixed points of the evolution equations in the Hartree
approximation. The form of the profile depends explicitly on the initial
ensemble. While the truncated evolution equations do not seem to be able to get
away from the fixed point, the full nonlinear evolution shows thermalization
with a (surprisingly) slow relaxation.
