We consider quasi-free stochastically positive ground and thermal states on
Weyl algebras in the imaginary time formulation. In particular, we obtain
a new derivation of a general form of thermal quasi-free state and give con
ditions when such a state is stochastically positive, i.e., when it defines
a periodic stochastic process with respect to imaginary time, a so-called
thermal process. Then we show that the thermal process completely determine
s modular structure canonically associated with the quasi-free thermal stat
e on Weyl algebra. We discuss a variety of examples connected with free qua
ntum field theories on globally hyperbolic stationary space-times and model
s of quantum statistical mechanics. (C) 1998 American Institute of Physics.
[S0022-2488(98)01712-5].