On the Relationship Between Extended Thermodynamics and the Wave Approach to Thermodynamics

A comparative analysis of two formulations of nonlinear irreversible processes is performed. We first disclose the difference between the well known OnsagerMachlup linear theory and the wave approach to thermodynamics (WAT) introduced by Gyarmati. We then discuss the essential content of the goal and postulates of extended irreversible thermodynamics (EIT) and compare them with those of WAT. From this comparison the differences, scope and limitations of each theory follow and the precise special conditions under which both theories yield similar results are identified. Finally, the more general type of constitutive equations that EIT can yield is illustrated by studying the behaviour of a nonlinear heat conductor. Introduction Undoubtedly, linear irreversible thermodynamics (LIT) strongly supported by the Onsager reciprocity relations which stem directly from the microscopic equations of motion obeyed by the particles composing a thermodynamic system, constitutes the so far a unique and acceptable framework for dealing with nonequilibrium phenomena [1-3]. In the early fifties, Onsager and Machlup [4] made a thorough revision of the underlying postulates of the theory using the concept of fluctuations in the thermodynamic variables of equilibrium systems in which after a criticism of the original version made by Casimir [5], they also included the presence of variables Which are odd under time reversal. In spite of the indisputable elegance and generality of the theory, such generalization still excluded from the theory systems in which the fluxes are not time derivatives of the fluctuations of the local extensive thermodynamic quantities nor the generalized forces are the derivatives of the entropy with respect to those fluctuations. Such phenomena like hydrodynamics, conduction of electricity and others had to be dealt with in a different way, without modifying the basic nature J. Non-Equilib. Thermodyn. , Vol.13, 1988, No. 1 Copyright © 1988 Walter de Gruyter · Berlin · New York 82 L. S. Garda-Colin, R. F. Rodriguez of the original postulates themselves [6-8]. In either or both versions, the theory has proved to be of a great value to describe within a thermodynamic context those phenomena which represent small deviations with respect to the state of global equilibrium. Also, the Onsager reciprocity relations have been confirmed experimentally in a wide class of systems [9]. Inspired by the success of the Onsager-Machlup (OM) formulation of the theory a number of efforts have been made to extend its range of validity beyond the restriction imposed by the linear laws coupling the forces to the fluxes [10]. We are concerned in this paper with one such effort namely, that advanced by Gyarmati in the form presented almost ten years ago [11]. The proponents of this theory, regardless of its intrinsic values, assert among other things, that it is at grips with the OM formalism for two reasons, one that the generalized constitutive laws induced into the theory are a consequence of the OM formalism and secondly, that the reciprocity relations are obeyed. The other assertion is that another approach to macroscopic non-equilibrium phenomena now known as extended irreversible thermodynamics (BIT) [12,13] is just a particular case of Gyarmati's approach. Neither statements are correct. Gyarmati's approach, based in a well defined set of assumptions is an internally consistent theory which constitutes, together with the results it leads to, an undeniable improvement over LIT. But as we show here, the theory is not related in any way, except formally, to OM and neither contains EIT as a particular case, in fact the situation in this matter is precisely the opposite. 1.