On Entropy Production in Informational Statistical Thermodynamics

We consider the question of the existence of a generalized H-theorem in the context of the variational method in the information-theoretical approach that generates the nonequilibrium statistical operator formalism. After brie y reviewing how the latter provides mechano-statistical foundations for phenomenological irreversible thermodynamics, the socalled Informational Statistical Thermodynamics, we discuss how dissipative phenomena are accounted for by the procedure. Such e ects are related to a generalized H-theorem and a weak criterion of positive entropy production. These results are a consequence of the de nition of a coarse-grained statistical entropy, resulting from the projection of the full nonequilibrium distribution function on the subspace of the slow relaxing dynamical quantities, that are appropriate for the description of the irreversible evolution of the system from the state of initial preparation.