  We discuss the classical limit for the long-distance (``soft'') modes of a
quantum field when the hard modes of the field are in thermal equilibrium. We
address the question of the correct semiclassical dynamics when a momentum
cut-off is introduced. Higher order contributions leads to a stochastic
interpretation for the effective action in analogy to Quantum Brownian Motion,
resulting in dissipation and decoherence for the evolution of the soft modes.
Particular emphasis is put on the understanding of dissipation. Our discussion
focuses mostly on scalar fields, but we make some remarks on the extension to
gauge theories.
