  A fluid analog of the information flux in the phase-space associated to
purity and von Neumann entropy are identified in the Weyl-Wigner formalism of
quantum mechanics. Once constrained by symmetry and positiveness, the
encountered continuity equations provide novel quantifiers for non-classicality
(non-Liouvillian fluidity) given in terms of quantum decoherence, purity and
von Neumann entropy fluxes. Through definitions in the Weyl-Wigner formalism,
one can identify the quantum fluctuations that distort the classical-quantum
coincidence regime, and the corresponding quantum information profile, whenever
some bounded $x-p$ volume of the phase-space is specified. The dynamics of
anharmonic systems is investigated in order to illustrate such a novel paradigm
for describing quantumness and classicality through the flux of quantum
information in the phase-space.
