Statistical-Mechanical Foundations for a Generalized Thermodynamics of Dissipative Processes

Abstract

A statistical‐mechanical formalism for nonequilibrium systems, namely the nonequilibrium statistical operator method, provides microscopic foundations for a generalized thermodynamics of dissipative processes. This formalism is based on a unifying variational approach that is considered to be encompassed in Jaynes' Predictive Statistical Mechanics and principle of maximization of the statistical‐informational entropy. Within the framework of the statistical thermodynamics that follows from the method, we demonstrate the existence of generalized forms of the theorem of minimum (informational) entropy production, the criterion for evolution, and the thermodynamic (in)stability criterion. The formalism is not restricted to local equilibrium but, in principle, to general conditions (its complete domain of validity is not yet fully determined). A H‐theorem associated to the formalism is presented in the form of an increase of the informational entropy along the evolution of the system. Some of the results are illustrated in an application to the study of a model for a photoexcited direct‐gap semiconductor.

The role of nonequilibrium thermo-mechanical statistics in modern technologies and industrial processes: an overview

“…They are related to the basic set of macro-variables by the relations (which can be considered as the equations of state in arbitrary non-equilibrium conditions [3,4,[13][14][15][16])…”

“…A complete description of the NESEF foundations for Irreversible Thermodynamics is available in Refs. [13][14][15][16].…”

“…The old difficulty with this sought after connection, which resided into looking exclusively at the microscopicmechanicist level of Physics, disappears when one begins to consider the macroscopic level of Physics. An important role is played by the thermodynamics of nonlinear nonequilibrium open dissipative systems, as it is the Informational-Statistical Thermodynamics, build on the basis of the NESEF [13][14][15][16], already mentioned in Section III. NESEF has been applied to the determination of the complex behavior that may result in biopolymers, namely, Fröhlich-Bose-Einstein-like condensation and propagation of Davidov's solitary-wave-like excitations, which are of relevance in Bioenergetics.…”

“…Nonlinearity (in the kinetic equations providing the evolution laws of the macroscopic state of the system) comes to have a relevant role, and with it enters into play the disciplines of Synergetic and Self-Organization [8,9] associated to systems with complex behavior (for short, complex systems); namely, formation of coherent structures organized at a macroscopic level (space, time, or functional organization), as it is the case of the omnipresent laser or life in the biosphere [10,11]. Finally, it needs be also considered the Mesoscopic Physics [12][13][14][15][16], necessary to deal with processes in nanometric scale in space and femto-second scale in time [17][18][19][20][21][22], the case of the so-called fractal structures [23], the emerging area of soft matter [24], and so on.…”

Ensemble formalism for nonequilibrium systems and an associated irreversible statical thermodynamics

“…We notice that Thermostatics, Classical Irreversible Thermodynamics and Extended Irreversible Thermodynamics are encompassed in Informational Statistical Thermodynamics, which gives them a microscopic foundation. Moreover, Generalized Nonequilibrium Thermodynamics (that is, the extension of Classical Irreversible Thermodynamics to the nonlinear domain) is also contained within the informational-statistical theory [120]. Recent attempts to improve on the construction of IST are reported in Refs.…”