Contributions to the Theory of Thermostated Systems

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.