  In this paper, a theory for systems in contact with a thermal reservoir is
developed. We call such systems "thermostated systems." Interest in these
systems has been vigorous for about the last 20 years and is illustrated by the
Crooks theorem and the Jarzinski equality, two results for the description of
systems in full phase space where all coordinates and momenta may be followed
through time. These fundamental results follow from the behavior of Markovian
systems in phase space for which path integral expressions can be derived from
the Smoluchowski equation valid for Markovian systems.
