  We propose a generalization of classical statistical mechanics which
describes the behavior of dissipative systems placed in contact with a heat
bath. In contrast to conventional statistical mechanics, which assigns
probabilities to the states of the system, the generalized theory assigns
probabilities to the trajectories of the system. The conditional probability of
pairs of states at two different times is given by a path integral. We present
two simple analytically-tractable examples which illustrate the predicted
effect of temperature on the mean trajectories, hysteresis and drift of the
system.
