Stochastic phase spaces and master Liouville spaces in statistical mechanics

The concept of probability space is generalized to that of stochastic probability space. This enables the introduction of representations of quantum mechanics on stochastic phase spaces. The resulting formulation of quantum statistical mechanics in terms of -distribution functions bears a remarkable resemblance to its classical counterpart. Furthermore, both classical and quantum statistical mechanics can be formulated in one and the same master Liouville space overL²(). A joint derivation of a classical and quantum Boltzman equation provides an illustration of the practical uses of these formalisms.Supported in part by an NRC grant.