On Entropy Production in Informational Statistical Thermodynamics

Abstract

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 w eak criterion of positive e n tropy 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.

Nonequilibrium Statistical Operator for Systems of Finite Size

“…On its basis the information statistical thermodynamics is formulated [26][27][28][29][30][31][32][33]. In works [26][27][28][29][30][31][32][33] the assumptions made when introducing NESOM are in details described.…”

“…Nonequilibrium statistical operator method (NESOM) [16][17][18][19][20][21][22][23][24][25] turned to be an effective tool in the solving the nonequilibrium problems. On its basis the information statistical thermodynamics is formulated [26][27][28][29][30][31][32][33]. In works [26][27][28][29][30][31][32][33] the assumptions made when introducing NESOM are in details described.…”

“…is the operator of entropy production [20,21,[29][30][31][32][33]. It corresponds to absence of fixing of the initial moment of time and averaging on t 0 [21] (relations (4), (6); in the second argument y=τ).…”

“…The expressions for average on ρ(t) of meaning ln (1-B) are obtained in [29][30][31][32][33]. Averaging (21) and (25) [35].…”