  Using the influence functional formalism, classical equations of motion for
the O(N) model are derived in the presence of a heat bath, in both the
symmetric phase as well as the phase of spontaneously broken symmetry. The heat
bath leads to dissipation and fluctuation terms in the classical equations of
motion, which are explicitly computed to lowest order in perturbation theory.
In the broken phase these terms are found to be large for the sigma field, even
at zero temperature, due to the decay process sigma -> pi pi, while they are
small for the pi fields at temperatures below T_c = 160 MeV. It is shown that
in large volumes the presence of dissipation and fluctuations suppresses the
formation of disoriented chiral condensates (DCC's). In small volumes, however,
fluctuations become sufficiently large to induce the formation of DCC's even if
chiral symmetry has not been restored in the initial stage of the system's
evolution.
