  The nonperturbative real-time evolution of quantum fields out of equilibrium
is often solved using a mean-field or Hartree approximation or by applying
effective action methods. In order to investigate the validity of these
truncations, we implement similar methods in classical scalar field theory and
compare the approximate dynamics with the full nonlinear evolution. Numerical
results are shown for the early-time behaviour, the role of approximate fixed
points, and thermalization.
