The informational-statistical-entropy operator in a nonequilibrium ensemble formalism

We study the eigenvalue spectrum of the informational-statistical-entropy operator, a quantity that plays a fundamental role in the nonequilibrium statistical operator method. We obtain explicit expressions for the informational entropy for inhomogeneous nonequilibrium (dissipative) systems, relevant for the study of its nonclassical nonlinear hydrodynamics. Expressions for the single-particle dynamical matrix and, in particular, for the distribution functions of quasi-particles, in conditions arbitrarily away from equilibrium, are also derived. We apply the results considering some aspects of the hydrodynamics of a Fermion system in weak interaction with a thermal bath of Bosons.