We present a general formalism for studying the effects of dynamical
heterogeneity in open quantum systems. We develop this formalism in the state
space of density operators, on which ensembles of quantum states can be
conveniently represented by probability distributions. We describe how this
representation reduces ambiguity in the definition of quantum ensembles by
providing the ability to explicitly separate classical and quantum sources of
probabilistic uncertainty. We then derive explicit equations of motion for
state space distributions of both open and closed quantum systems and
demonstrate that resulting dynamics take a fluid mechanical form analogous to a
classical probability fluid on Hamiltonian phase space, thus enabling a
straightforward quantum generalization of Liouville's theorem. We illustrate
the utility of our formalism by analyzing the dynamics of an open two-level
system using the state-space formalism that are shown to be consistent with the
derived analytical results