Extended irreversible thermodynamics revisited (1988–98

2008

Current frontiers of technology require generalized transport equations incorporating memory, non-local effects, and non-linear effects. Extended Irreversible Thermodynamics provides such transport equations in a form compatible with the second law of thermodynamics, and that, for low frequency and short mean-free paths, reduce to the classical transport equations. Here we present the basic concepts of extended irreversible thermodynamics, namely, the fluxes as independent variables, and their evolution equations as generalized transport equations obeying the second law of thermodynamics. We show that these equations cover a rich phenomenology in heat transport, including thermal waves, phonon hydrodynamics, ballistic transport, and saturation in the fluxes for high values of the thermodynamic forces.

Pramana-journal of Physics, 1999

It is reiterated that without a Gibbs-Duhem equation no thermodynamic description of irreversible and reversible processes exists. It is shown with the help of Gibbs-Duhem equation of extended irreversible thermodynamics that the physical contents of intensive quantities, the temperature and the pressure, do not change in going from reversible to irreversible processes. This confirms well with the earlier demonstrations of Eu and García-Colín.

2012

There exist different formulations of the irreversible thermodynamics. Depending on the distance from the equilibrium state and on the characteristic time the main theories are the classical theory (CIT), the thermodynamics with internal variables (IVT) and the extended theory (EIT). Sometimes it is not easy to choose the proper theory and to use it efficiently with respect to applied problems considering different fields of interest. Especially EIT is explained mainly for very special choice of the dissipative fluxes under specific presumptions. The paper tries to formulate EIT and IVT in a simple, unified but general enough form. The basic presumptions for EIT are shown and discussed, further a possible generalization is proposed. The formulation allows the integration of IVT and EIT even for the mixture of chemically interacting components and diffusion. The application of the formulation is demonstrated on an example.

Aapp Physical Mathematical and Natural Sciences, 2008

What is the physical significance of entropy? What is the physical origin of irreversibility? Do entropy and irreversibility exist only for complex and macroscopic systems? Most physicists still accept and teach that the rationalization of these fundamental questions is given by Statistical Mechanics. Indeed, for everyday laboratory physics, the mathematical formalism of Statistical Mechanics (canonical and grand-canonical, Boltzmann, Bose-Einstein and Fermi-Dirac distributions) allows a successful description of the thermodynamic equilibrium properties of matter, including entropy values. However, as already recognized by Schrödinger in 1936, Statistical Mechanics is impaired by conceptual ambiguities and logical inconsistencies, both in its explanation of the meaning of entropy and in its implications on the concept of state of a system. An alternative theory has been developed by Gyftopoulos, Hatsopoulos and the present author to eliminate these stumbling conceptual blocks while maintaining the mathematical formalism so successful in applications. To resolve both the problem of the meaning of entropy and that of the origin of irreversibility we have built entropy and irreversibility into the laws of microscopic physics. The result is a theory, that we call Quantum Thermodynamics, that has all the necessary features to combine Mechanics and Thermodynamics uniting all the successful results of both theories, eliminating the logical inconsistencies of Statistical Mechanics and the paradoxes on irreversibility, and providing an entirely new perspective on the microscopic origin of irreversibility, nonlinearity (therefore including chaotic behavior) and maximal-entropy-generation nonequilibrium dynamics. In this paper we discuss the background and formalism of Quantum Thermodynamics including its nonlinear equation of motion and the main general results. Our objective is to show in a not-too-technical manner that this theory provides indeed a complete and coherent resolution of the century-old dilemma on the meaning of entropy and the origin of irreversibility, including Onsager reciprocity relations and maximal-entropy-generation nonequilibrium dynamics, which we believe provides the microscopic foundations of heat, mass and momentum transfer theories, including all their implications such as Bejan's Constructal Theory of natural phenomena.

Comptes Rendus Physique, 2007

New definitions of entropy and temperature for uniform systems that fast exchange heat with the environment are considered. Instead of the known local equilibrium hypothesis, a local uniformity hypothesis is proposed. Within the proposed formalism of extended thermodynamics of irreversible processes, dual-phase-lag transfer equations are obtained. To cite this article:

Physical Review A, 1985

The thermodynamic implications of the first deviations with respect to the classical hydrodynamic behavior in high-frequency, short-wavelength phenomena are examined. The constitutive equations arising from an extended irreversible-thermodynamic formalism taking into account spatial inhomogeneities in the space of state variables are compared with those used in generalized hydrodynamics. The so-called exponential model for the memory function of the transverse-velocity correlation function is derived under the assumptions of extended irreversible thermodynamics only. Furthermore, it is also shown how more complicated memory functions can be derived. The results are carefully analyzed and compared with some microscopic derivations.

Physics Letters A, 1985

The non-linear relationship that holds between the chemical flux and the chemical affinity for chemical reactions taking place amongst ideal gases or solutions in homogeneous phases is shown to belong to the framework of extended non-equilibrium thermodynamics. Its generalization to include non-ideal systems, as well as other features, are also discussed.

Starting from the generalized Gibbs equation of extended irreversible thermodynamics, we define a thermodynamic potential that provides a suitable description of the fluctuations of the hydrodynamical dissipative fluxes when it is used in an expression analogous to the classical Einstein formula for the probability of fluctuations. In the limit of vanishing relaxation times, our results coincide with those of Landau-Lifshitz. The effect of the rapid normal modes is taken into account as a stochastic noise in the evolution equations of the dissipative fluxes, and their covariance matrix is found from a fluctuation-dissipation theorem.

Physica A: Statistical Mechanics and its Applications, 2003

PII of original article S0378-4371(02)00491-0.

The status of heat and work in nonequilibrium thermodynamics is quite confusing and nonunique at present with conflicting interpretations even after a long history of the first law dE(t) = d e Q(t) − dW e (t) in terms of exchange heat and work, and is far from settled. Moreover, the exchange quantities lack certain symmetry (see text). By generalizing the traditional concept to also include their time-dependent irreversible components d i Q(t) and d i W (t) allows us to express the first law in a symmetric form dE(t) = dQ(t) − dW (t) in which dQ(t) and work dW (t) appear on equal footing and possess the symmetry. We prove that d i Q(t) ≡ d i W (t); as a consequence, irreversible work turns into irreversible heat. Statistical analysis in terms of microstate probabilities p i (t) uniquely identifies dW (t) as isentropic and dQ(t) as isometric (see text) change in dE(t), a result known in equilibrium. We show that such a clear separation does not occur for d e Q(t) and dW e (t). Hence, our new formulation of the first law provides tremendous advantages and results in an extremely useful formulation of non-equilibrium thermodynamics, as we have shown recently [Phys. Rev. E 81, 051130 (2010); ibid 85, 041128 and 041129 (2012)]. We prove that an adiabatic process does not alter p i. All these results remain valid no matter how far the system is out of equilibrium. When the system is in internal equilibrium, dQ(t) ≡ T (t)dS(t) in terms of the instantaneous temperature T (t) of the system, which is reminiscent of equilibrium, even though, neither d e Q(t) ≡ T (t)d e S(t) nor d i Q(t) ≡ T (t)d i S(t). Indeed, d i Q(t) and d i S(t) have very different physics. We express these quantities in terms of d e p i (t) and d i p i (t), and demonstrate that p i (t) has a form very different from that in equilibrium. The first and second laws are no longer independent so that we need only one law, which is again reminiscent of equilibrium. The traditional formulas like the Clausius inequality d e Q(t)/T 0 < 0, ∆ e W < −∆ [E(t − T 0 S(t))], etc. become equalities dQ(t)/T (t) ≡ 0, ∆W = −∆ [E(t − T (t)S(t)], etc, a quite remarkable but unexpected result in view of the fact that ∆ i S(t) > 0. We identify the uncompensated transformation N (t, τ) during a cycle. We determine the irreversible components in two simple cases to show the usefulness of our approach; here, the traditional formulation is of no use. Our extension bring about a very strong parallel between equilibrium and non-equilibrium thermodynamics, except that one has irreversible entropy generation d i S(t) > 0 in the latter.