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Phase-space features of the Wigner flow are examined so to provide a set ofcontinuity equations that describe the flux of quantum information in thephase-space. The reported results suggest that the non-classicality profile ofanharmonic (periodic) quantum systems can be consistently obtained in terms ofthe fluxes of probability, purity and von Neumann entropy. Extensions of thesuch phase-space quantifiers are also investigated in the context of theso-called R\'enyi entropy.

Phase-space continuity equations for quantum decoherence, purity, von Neumann and R\'enyi entropies