  The aim of this paper is two-fold: in probing the statistical mechanical
properties of interacting quantum fields, and in providing a field theoretical
justification for a stochastic source term in the Boltzmann equation. We start
with the formulation of quantum field theory in terms of the Schwinger - Dyson
equations for the correlation functions, which we describe by a
closed-time-path master ($n = \infty PI$) effective action. When the hierarchy
is truncated, one obtains the ordinary closed-system of correlation functions
up to a certain order, and from the nPI effective action, a set of
time-reversal invariant equations of motion. But when the effect of the higher
order correlation functions is included (through e.g., causal factorization--
molecular chaos -- conditions, which we call 'slaving'), in the form of a
correlation noise, the dynamics of the lower order correlations shows
dissipative features, as familiar in the field-theory version of Boltzmann
equation. We show that fluctuation-dissipation relations exist for such
effectively open systems, and use them to show that such a stochastic term,
which explicitly introduces quantum fluctuations on the lower order correlation
functions, necessarily accompanies the dissipative term, thus leading to a
Boltzmann-Langevin equation which depicts both the dissipative and stochastic
dynamics of correlation functions in quantum field theory.
