  We study under which conditions an overdamped regime can be attained in the
dynamic evolution of a quantum field configuration. Using a real-time
formulation of finite temperature field theory, we compute the effective
evolution equation of a scalar field configuration, quadratically interacting
with a given set of other scalar fields. We then show that, in the overdamped
regime, the dissipative kernel in the field equation of motion is closely
related to the shear viscosity coefficient, as computed in scalar field theory
at finite temperature. The effective dynamics is equivalent to a time-dependent
Ginzburg-Landau description of the approach to equilibrium in phenomenological
theories of phase transitions. Applications of our results, including a
recently proposed inflationary scenario called ``warm inflation'', are
discussed.
