On the definitions of entropy and temperature in the extended thermodynamics of irreversible processes

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: S.I. Serdyukov, C. R. Physique 8 (2007).     

On the relationship between fluctuating irreversible thermodynamics and “extended” irreversible thermodynamics

The relationship between fluctuating irreversible thermodynamics and theories of irreversible processes which include the thermodynamic fluxes as independent variables is explored. It is shown that the usual fluctuating linear theory of irreversible thermodynamics is a contraction of the extended theory. This contraction contains non-Markovian effects dependent upon the relaxation times associated with the thermodynamic fluxes. In the limit that these relaxation times are small, the extended theory is shown to be equivalent to the usual fluctuating thermodynamic theory. A critique of the extended theories is given from the point of view of the mechanistic statistical theory of irreversible processes.     

About some effects of linear transformation of fluxes and forces in extended irreversible thermodynamics

The effects of linear transformations of fluxes and forces in the framework of EIT are examined.     

The kinetic foundation of extended irreversible thermodynamics revisited

Extended irreversible thermodynamics (EIT) has been used mainly to study the short-time behavior of fluids and some other systems. It has also been shown how the structure of the equations of motion constructed for the so-called relaxation variables coincides with those obtained by means of Grad's method in kinetic theory. In this work we calculate the generalized entropy from the one-particle distribution function up to 26 moments. We find that the characteristics of such entropy and the equations of motion for the relaxing variables are supported by the kinetic theory. This is not the case for the hierarchical relaxation hypothesis which is used in the applications of EIT to the generalized hydrodynamic regime.On temporary leave at the Universidad Iberoamericana, Mexico.     

On the entropy contribution to thermodynamics of melted flux liquids

The lattice models of thermally disordered flux line system are studied by the random walk method. We formulate rigorously the 2D model having an exact solution. In three dimensions the method leads to the generalized Bethe approximation. The critical behavior of both thermodynamic and correlation functions nearH _c1 is considered. An examination of a possible transition between entangled and disentangled phases is done.     

Statistical thermodynamics from the point of view of statistical theory of estimation

An essentially statistical theory of thermodynamics is developed on the basis of additivity and conservation laws of fundamental entities of thermodynamics. The theory developed by Dutta (1953–59) stresses first the importance of the statistical theory of estimation in the statistical foundation of thermodynamics. The method of finding the distribution law is based on the principle similar to that of Bayes' rule in probability theory and the method of maximum-likelihood estimation of mathematical statistics. The model used is macroscopic in nature and the laws of microscopic distributions (M-B, B-E and F-D statistics) have been obtained by additional axiom regarding the constituents of the system. The object of the paper is to present an outline of the theory with some of its extensions to quantum macro-system and non-equilibrium thermodynamics.     

The extended mapping method and its applications for nonlinear evolution equations

The extended mapping method with a computerized symbolic computation is used to drive some new exact solutions of four nonlinear evolution equations in mathematical physics. As a result, many exact travelling wave solutions are obtained which include new solitary wave solutions, triangular and hyperbolic functions. Solutions in the limiting cases have also been studied. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.     

A new version of extended irreversible thermodynamics and dual-phase-lag model in heat transfer

For a system involving heat transfer, a new postulate of extended irreversible thermodynamics is suggested, which, in case of a stationary states, reduces to the local equilibrium hypothesis. On the basis of this postulate, a transport equation of the dual-phase-lag model of heat transfer is derived. In the proposed formalism, an extended evolution criterion generalizing the known Glansdorff–Prigogine criterion takes place.     

Nonlocal Lagrange formalism in the thermodynamics of irreversible processes: variational procedures for kinetic equations

This paper is concerned with generalizations of the known local Lagrange formalism of first order. It will be applied to kinetic equations like the Fokker-Planck equation and the Boltzmann equation. In the latter case nonlocal methods are necessary from the very beginning. Nevertheless, in the framework of Fréchet's formalism the calculations are as easy as in the classical local case.Furthermore, a rather general entropy concept can be established within nonlocal Lagrange formalism for irreversible systems. As a main result of this paper we derive within our general concept the known entropy balances of the Boltzmann theory and the Fokker-Planck theory, respectively. It will be emphasized that our general concept may be applied to a very wide class of irreversible systems, in principle.     

Variational principle for the thermodynamics of irreversible processes

A general variational principle equivalent to the balance equations is considered. Conditions of variation are based on stochastic ideas. A connection between the varied expression and the entropy is derived for both the relativistic case and the nonrelativistic approximation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 47–51, May, 1980.     

Entropy production and thermodynamics of nonequilibrium stationary states: a point of view

Entropy might be a not well defined concept if the system can undergo transformations involving stationary nonequilibria. It might be analogous to the heat content (once called "caloric") in transformations that are not isochoric (i.e., which involve mechanical work): it could be just a quantity that can be transferred or created, like heat in equilibrium. The text first reviews the philosophy behind a recently proposed definition of entropy production in nonequilibrium stationary systems. A detailed technical attempt at defining the entropy of a stationary states via their variational properties follows: the unsatisfactory aspects of the results add arguments in favor of the nonexistence of a function of state to be identified with entropy; at the same time new aspects and properties of the phase space contraction emerge.     

The application of the thermodynamics of irreversible processes to welding arcs

The self-regulation of an inert gas shielded metal welding arc is dealt with briefly. A thermodynamic equation is derived for the self-regulation of such an arc.

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Dynamical entropy and the third law of thermodynamics

We show that the third law of thermodynamics holds if the equilibrium states cluster appropriately in space and time uniformly for small temperatures. In this case, the entropy density and the dynamical entropy of the shift coincide. As an example in a one-dimensional lattice system with short-range interactions these cluster conditions are verified.Work supported in part by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, Project No. P6077P.     

Geometry from the spectral point of view

In this Letter, we develop geometry from a spectral point of view, the geometric data being encoded by a triple (A. H. D.) of an algebraA represented in a Hilbert spaceH with selfadjoint operatorD. This point of view is dictated by the general framework of noncommutative geometry and allows us to use geometric ideas in many situations beyond Riemannian geometry.

This paper is dedicated to the memory of J. Schwinger