  By using the quantum maximum entropy principle we formally derive, from a
underlying kinetic description, isothermal (hydrodynamic and diffusive) quantum
fluid equations for particles with Fermi-Dirac and Bose-Einstein statistics. A
semiclassical expansion of the quantum fluid equations, up to O(h^2)-terms,
leads to classical fluid equations with statistics-dependent quantum
corrections, including a modified Bohm potential. The Maxwell-Boltzmann limit
and the zero temperature limit are eventually discussed.
