  The non-equilibrium dynamics of the first stage of the reheating process,
that is dissipation via particle production is studied in scalar field theories
in the unbroken and in the broken symmetry phase. We begin with a perturbative
study to one loop and show explicitly that the mechanism of dissipation via
particle production cannot be explained with a simple derivative term in the
equation of motion. The dissipative contribution is non-local and there does
not exist a local (Markovian) limit at zero temperature. Furthermore, we show
that both an amplitude as well as a one-loop calculation present instabilities,
requiring a non-perturbative resummation. Within the same approximations, we
study an O(2) linear sigma model that allows to study dissipation by Goldstone
bosons.
  We find infrared divergences that require non-perturbative resummation in
order to understand the long-time dynamics. We obtain a perturbative
  Langevin equation that exhibits a generalized fluctuation-dissipation
relation, with non-Markovian kernels and colored noise. We then study a
  Hartree approximation and clearly exhibit dissipative effects related to the
thresholds to particle production. The asymptotic dynamics depends on the
coupling and initial conditions but does not seem to lead to exponential
relaxation. The effect of dissipation by Goldstone bosons is studied
non-perturbatively in the large N limit in an O(N) theory. Dissipation produced
by Goldstone bosons dramatically changes the picture of the phase transition.
We find the remarkable result that for ``slow-roll'' initial conditions (with
the expectation value of the field initially near the origin) the final value
of the expectation value of the scalar field is very close to its initial
value. We find that the minima of the effective action depend on the initial
conditions. We provide extensive numerical analysis of the dynamics.
