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General statistical ensembles in the Hamiltonian formulation of hybridquantum-classical systems are analyzed. It is argued that arbitrary probabilitydensities on the hybrid phase space must be considered as the class of possiblephysically distinguishable statistical ensembles of hybrid systems.Nevertheless, statistical operators associated with the hybrid system and withthe quantum subsystem can be consistently defined. Dynamical equations for thestatistical operators representing the mixed states of the hybrid system andits quantum subsystem are derived and analyzed. In particular, these equationsirreducibly depend on the total probability density on the hybrid phase space.

Statistical ensembles in Hamiltonian formulation of hybrid quantum-classical systems