  We study the full out-of-thermal-equilibrium dynamics of a relativistic
classical scalar field through a symmetry breaking phase transition. In these
circumstances we determine the evolution of the ensemble averages of the
correlation length and topological defect densities. This clarifies many
aspects of the non-perturbative dynamics of fields in symmetry breaking phase
transitions and allows us to comment on a quantitative basis on the canonical
pictures for topological defect formation and evolution. We also compare these
results to those obtained from the field evolution in the Hartree approximation
or using the linearized theory. By doing so we conclude about the regimes of
validity of these approximations.
