  In the previous papers (Kui\'{c} et al. in Found Phys 42:319-339, 2012;
Kui\'{c} in arXiv:1506.02622, 2015), it was demonstrated that applying the
principle of maximum information entropy by maximizing the conditional
information entropy, subject to the constraint given by the Liouville equation
averaged over the phase space, leads to a definition of the rate of entropy
change for closed Hamiltonian systems without any additional assumptions. Here,
we generalize this basic model and, with the introduction of the additional
constraints which are equivalent to the hydrodynamic continuity equations, show
that the results obtained are consistent with the known results from the
nonequilibrium statistical mechanics and thermodynamics of irreversible
processes. In this way, as a part of the approach developed in this paper, the
rate of entropy change and entropy production density for the classical
Hamiltonian fluid are obtained. The results obtained suggest the general
applicability of the foundational principles of predictive statistical
mechanics and their importance for the theory of irreversibility.
