  We investigate the dynamics of thermalization and the approach to equilibrium
in the classical phi^4 theory in 3+1 spacetime dimensions. The non-equilibrium
dynamics is studied by numerically solving the equations of motion in a light-
cone-like discretization of the model for a broad range of initial conditions
and energy densities.A smooth cascade of energy towards the ultraviolet is
found to be the basic mechanism of thermalization.After an initial transient
stage,at a time scale of several hundreds inverse masses,the squared of the
field gradient becomes larger than the nonlinear term and a stage of universal
cascade emerges. As the cascade progresses, the modes with higher wavenumbers
exhibit weaker and weaker nonlinearities well described by the Hartree
approximation while the infrared modes retain strong selfinteractions. Two
timescales for equilibration appears.For k^2><phi^2>(t) we observe an effective
thermalization with a time scale in the thousands of inverse masses and the
Hartree approximation holds. By effective thermalization we mean that the
observable acquires the equilibrium functional form with an effective time
dependent temperature Teff, which slowly decreases with time. Infrared modes
with k^2 < <phi^2>(t) equilibrate only by time scales in the millions of
inverse masses. Infrared modes with k^2 < <phi^2>(t) equilibrate only by time
scales in the millions.Virialization and the equation of state start to set
much earlier than effective thermalization.The applicability of these results
in quantum field theory for large occupation numbers and small coupling is
analyzed.
