The foundations of informational statistical thermodynamics revisited

The aim of this paper is to review the fundamental ideas of the underlying method behind informational statistical thermodynamics. This method is set forth to deal with phenomena that occur in nonequilibrium systems. The most significant aspects of this analysis are: (i) To show that Abel's theorem guarantees that in the asymptotic limit, the nonequilibrium statistical operator (NSO) obtained by MAXENT generates a stationary solution of the Liouville equation. This fact is consistent with the experimental behavior of an equilibrium system. (ii) Further, it is also shown how a Liouville equation with sources can be obtained by the NSO determined by MAXENT, whose formal solution proves that the general interpretation of Abel's theorem leading to memory effects is incorrect. Rather, this theorem introduces a time smoothing function in a time interval: t(0) = -infinity < t' < t(1) (t(1): initial time of an observation), which is to be understood as one that connects an adiabatic perturbation for t' < t(1). In fact, the memory effects appear in the evolution equations for the average values of the dynamical variables obtained by the NSO when these evolution equations are calculated up to second order in the perturbation Hamiltonian. (iii) Also, some criticisms that have been presented against MAXENT formalism are discussed and it is shown that they are inapplicable. Such criticisms are related to the memory effects and with the inconsistency of evolution equations for macrovariables with respect to the total energy conservation equation.