  We consider the non-equilibrium dynamics of a real quantum scalar field. We
show the formal equivalence of the exact evolution equations for the
statistical and spectral two-point functions with a fictitious Langevin process
and examine the conditions under which a local Markovian dynamics is a valid
approximation. In quantum field theory, the memory kernel and the noise
correlator typically exhibit long time power laws and are thus highly
non-local, thereby questioning the possibility of a local description. We show
that despite this fact, there is a finite time range during which a local
description is accurate. This requires the theory to be (effectively) weakly
coupled. We illustrate the use of such a local description for studies of
decoherence and entropy production in quantum field theory.
