Classical statistical mechanics, as well as quantum statistical mechanics, are both acknowledgedly statistical theories even if one subscribes to the conventional point of view about the intrinsically disparate natures of classical and quantum mechanics, respectively. Yet, the conventional mathematical frameworks for these two theories are remarkably dissimilar even at the most fundamental level of description of states of ensembles: in the classical case states are described by distribution functions ƒ(q, p) on phase space, whereas in the quantum case they are given by density operators ρ.