MICROSCOPIC APPROACH TO IRREVERSIBLE THERMODYNAMICS .3. GENERALIZED CONSTITUTIVE-EQUATIONS

This paper and the following one are part of a planned sequence of contributions on the question of the mechano-statistical foundations of irreversible thermodynamics and generalized hydrodynamics, based on the nonequilibrium statistical operator method via the information entropy ensemble. With this we introduce what can be termed Informational Statistical Thermodynamics. The series of papers amounts to an extension and detailed application of a general formalism initiated in papers I and II (quoted in references [12] and [13]) to study the time evolution of the variables selected to describe the nonequilibrium macroscopic states of an N-body system. These variables are to be chosen according to some criteria which the observer uses to define such states, but are otherwise arbitrary. We consider here the set that includes the ordinary fluxes of Linear Irreversible Thermodynamics (LIT), thus raising these variables to the status of state variables, to recover the results comprising the basis of what is now known as Extended Irreversible Thermodynamics (EIT). The time evolution equations for the fluxes are shown to be of the type of generalized Mori-Langevin equations that are nonlinear and nonlocal in space and in time. Under appropriate approximations such equations are reduced to those of the so-called Maxwell-Cattaneo-Vernotte type contained in EIT, which are generalizations of the usual constitutive equations of LIT. In fact, taking a linear approximation in the fluxes and a local-in-time-approach, and considering a quasi-steady state, the equations represent nonlocal-in-space generalized constitutive-like equations for the fluxes.