Extended irreversible thermodynamics revisited (1988-98)

Abstract

We review the progress made in extended irreversible thermodynamics during the ten years that have elapsed since the publication of our first review on the same subject (Rep. Prog. Phys. 1988Phys. 51 1105. During this decade much effort has been devoted to achieving a better understanding of the fundamentals and a broadening of the domain of applications. The macroscopic formulation of extended irreversible thermodynamics is reviewed and compared with other non-equilibrium thermodynamic theories. The foundations of EIT are discussed on the bases of information theory, kinetic theory, stochastic phenomena and computer simulations. Several significant applications are presented, some of them of considerable practical interest (non-classical heat transport, polymer solutions, non-Fickian diffusion, microelectronic devices, dielectric relaxation), and some others of special theoretical appeal (superfluids, nuclear collisions, cosmology). We also outline some basic problems which are not yet completely solved, such as the definitions of entropy and temperature out of equilibrium, the selection of the relevant variables, and the status to be reserved to the H -theorem and its relation to the second law. In writing this review, we had four objectives in mind: to show (i) that extended irreversible thermodynamics stands at the frontiers of modern thermodynamics;(ii) that it opens the way to new and useful applications; (iii) that much progress has been achieved during the last decade, and (iv) that the subject is far from being exhausted.

Constitutive equations for heat conduction in nanosystems and nonequilibrium processes: an overview

“…Extensions of Eq. (1) to the nonlinear regime may be obtained in the framework of Extended Irreversible Thermodynamics (EIT) [6,7,21,27,28], a theory which upgrades the dissipative fluxes to the rank of independent thermodynamic variables [10,22,[29][30][31], while nonlinear generalizations of Eq. (2) have been obtained either in EIT [5], or in the framework of the thermomass theory [12][13][14], which also pays a special attention to nonlinear terms in the heat transport equation.…”

Supersymmetry model of a binary mixture with noise of the diffusion flux

“…(2), angular brackets denote averaging over ζ(r, t) and T is the noise intensity being the temperature. With introducing measure units 2 for the time t, coordinate r, specific free energy f and stochastic force ζ , respectively, Eq. (1) takes the simple form…”

“…Particularly, one of the main focuses of theoretical investigation was to describe non-equilibrium systems at high frequency or high speed of perturbations (see overviews [1,2] and references therein). Experimentally, non-equilibrium binary systems under diffusion may exist in rapidly quenched liquid mixtures, processes with shock waves, deeply supercooled phases, and, generally, in systems under rapid phase transformations.…”

“…Experimentally, non-equilibrium binary systems under diffusion may exist in rapidly quenched liquid mixtures, processes with shock waves, deeply supercooled phases, and, generally, in systems under rapid phase transformations. Using extended thermodynamical theory [1,2], a role of relaxation and inertial processes has been outlined in recent models [3,4]. As a basic idea of these models, thermodynamically independent variables were extended by the set of fast variables.…”

Memory effect and fast spinodal decomposition

“…Although the diffusion equation has broad applicability, there exist the applicability limitations. First, the diffusion equation does not obey causality [1]. Let us consider the following telegraph equation,…”