  A basic aspect of the kinetic descriptions of incompressible fluids based on
an inverse kinetic approaches is the possibility of satisfying an H-theorem.
This property is in fact related to the identification of the kinetic
distribution function with a probability density in an appropriate phase space.
Goal of this investigation is to analyze the conditions of validity of an
H-theorem for the inverse kinetic theory recently proposed by Ellero and
Tessarotto [2004, 2005]. It is found that the time-dependent contribution to
the kinetic pressure, characteristic of such a kinetic model, can always be
uniquely defined in such a way to warrant the constancy of the entropy.
