José Casas-Vázquez

Temperature in non-equilibrium states: a review of open problems and current proposals

The conceptual problems arising in the definition and measurement of temperature in non-equilibrium states are discussed in this paper in situations where the local-equilibrium hypothesis is no longer satisfactory. This is a necessary and urgent discussion because of the increasing interest in thermodynamic theories beyond local equilibrium, in computer simulations, in non-linear statistical mechanics, in new experiments, and in technological applications of nanoscale systems and material sciences. First, we briefly review the concept of temperature from the perspectives of equilibrium thermodynamics and statistical mechanics. Afterwards, we explore which of the equilibrium concepts may be extrapolated beyond local equilibrium and which of them should be modified, then we review several attempts to define temperature in non-equilibrium situations from macroscopic and microscopic bases. A wide review of proposals is offered on effective non-equilibrium temperatures and their application to ideal and real gases, electromagnetic radiation, nuclear collisions, granular systems, glasses, sheared fluids, amorphous semiconductors and turbulent fluids. The consistency between the different relativistic transformation laws for temperature is discussed in the new light gained from this perspective. A wide bibliography is provided in order to foster further research in this field.

Extended irreversible thermodynamics revisited (1988-98)

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. Frog. Phys. 1988 51 1105-72). 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.

Thermodynamics of fluids under flow

From the contents: Non-equilibrium Thermodynamics and Rheology.- Ideal Gases.- Non-ideal Fluids.- Polymeric Solutions.- Non-equilibrium Chemical Potential and Shear-Induced Effects.- Comparison Between Thermodynamical and Dynamical Approaches.- Thermodynamic Couplings Between Flow and Diffusion.- Chemical Reactions Under Flow.- Concluding Remarks and Perspectives.- Appendices: A. Survey of Experimental Information.- B. Liquid Crystals.- C. Summary of Vector and Tensor Notation.- D. Useful Integrals in the Kinetic Theory of Gases.- E. Some Physical Constants.- Subject Index.

On the foundations of extended irreversible thermodynamics

A theory of macroscopic systems which takes as independent variables the slow (conserved) ones plus the fast dissipative fluxes is carefully analyzed at three levels of description: macroscopic (thermodynamic), microscopic (projection operators) and mesoscopic (fluctuation theory). Such a description is compared with the memory function approach based only on the conserved variables. We find that the first theory is richer and wider than the second one, and some misunderstandings in this connection are clarified and discussed.

A phenomenological scaling approach for heat transport in nano-systems

A phenomenological approach of heat transfer in nano-systems is proposed, on the basis of a continued-fraction expansion of the thermal conductivity, obtained within the framework of extended irreversible thermodynamics. Emphasis is put on the transition from the diffusive, collision-dominated heat transport to the ballistic heat transport, as a function of the mean free path and the length of the system.

Weakly Nonlocal And Nonlinear Heat Transport In Rigid Solids

A weakly nonlocal and nonlinear theory of heat conduction in rigid bodies is proposed. The constitutive equations generalize these of Fourier, Maxwell-Cattaneo and Guyer-Krumhansl. The proposed model uses the fundaments and the technique of extended irreversible thermodynamics. The main conclusion is that the presence of nonlocal terms in the transport equation for the heat flux implies a modification of the entropy flux; the latter is no longer given by its classical expression, i.e. the heat flux divided by the temperature, but contains extra contributions which are nonlinear in the heat flux and its gradient. These results arise as compatibility conditions with the second law of thermodynamics. A nonequilibrium temperature depending on the heat flux and generalizing the local equilibrium temperature is also emerging naturally from the formalism.

Thermodynamic variables in the context of a nonequilibrium statistical ensemble approach

We consider the question of the definition of thermodynamic-like variables in the context of a statistical thermodynamics, which is a large generalization of Gibbs statistical thermostatics and linear and local-equilibrium classical irreversible thermodynamics. It is based on a nonequilibrium ensemble approach known as the nonequilibrium statistical operator method. Some of these quasithermodynamic variables are characteristic of the nonequilibrium state and go to zero in the limit of local or global equilibrium, but others go over the thermodynamic variables that are present in such a limit. We consider in particular temperature-like variables for the different subsystems of the sample. For illustration we apply the theory to the study of optical properties of highly photoexcited plasma in semiconductors, following a good agreement between theory and experimental data. It is shown that high-resolution spectroscopy provides an excellent experimental testing ground for corroboration of the theoretical concepts, and a quite appropriate way for characterizing and measuring nonequilibrium thermodynamic-like variables.

Nonequilibrium absolute temperature, thermal waves and phonon hydrodynamics

Abstract It is shown that the nonequilibrium absolute temperature of extended irreversible thermodynamics may lead to possibly observable consequences in the propagation of thermal waves in nonequilibrium solids and in Poiseuille phonon flow.

On the selection of the state space in nonequilibrium thermodynamics

We address here the question of the choice and interpretation of state variables in the thermodynamical description of systems arbitrarily away from equilibrium. It is presented a discussion of the topic in the framework of informational statistical thermodynamics, an approach based on Gibbs algorithm for nonequilibrium dissipative systems, which provides mechano-statistical foundations to phenomenological theories of irreversible thermodynamics. The theory is applied in the case of a particular system consisting of the mobile carriers in a highly excited photo-injected plasma in semiconductors. The concepts and results thus obtained are tested against experimental data in time-resolved and time-integrated optical laser spectroscopy. It is shown how equilibrium thermodynamic variables are evidenced and measured in such experiments. It is also discussed the influence on them of the inclusion of dissipative fluxes among the basic variables.

Evolution of dissipative processes via a statistical thermodynamic approach. I. Generalized Mori–Heisenberg–Langevin equations

Within the scope of a nonequilibrium statistical ensemble formalism we derive a hierarchy of equations of evolution for a set of basic thermo-hydrodynamic variables, which describe the macroscopic nonequilibrium state of a fluid of bosons. This set is composed of the energy density and number density and their fluxes of all order. The resulting equations can be considered as far-reaching generalizations of those in Mori’s approach. They involve nonlocality in space and retro-effects (i.e. correlations in space and time respectively), are highly nonlinear, and account for irreversible behavior in the macroscopic evolution of the system. The different contributions to these kinetic equations are analyzed and the Markovian limit is obtained. In the follow up article we consider the nonequilibrium thermodynamic properties that the formalism provides.