  We investigate an undamped random phase-space dynamics in deterministic
external force fields (conservative and magnetic ones). By employing the
hydrodynamical formalism for those stochastic processes we analyze microscopic
kinetic-type "collision invariants" and their relationship to local
conservation laws (moment equations) in the fully nonequlibrium context. We
address an issue of the continual heat absorption (particles "energization") in
the course of the process and its possible physical implementations.
