IRREVERSIBLE PROCESSES AND PHYSICAL INTERPRETATION OF RATIONAL THERMODYNAMICS

The paper contains a synthesis of recent developments that have extended the domain of validity of the classical version of thermodynamics of irreversible processes and generalized its methods. The presentation is largely based on the recognition of the factthat the real, nonequilibrium state of a material particle undergoing an irreversible process always remains close to a properly selected constrained equilibrium state — known as the accompanying state — which is described by the usual variables (deformation gradient and internal energy) and an adequate set of internal variables to which a physical meaning can be attached. The selection of these internal variables depends on the intended level of description and on the pair material-process being analyzed. The preceding circumstances allow us to write down a Gibbs equation for the accompanying state of the system which, together with the conservation laws, makes it possible to calculate the volumetric rate of production of accompanying entropy. It is recognized that the latter must be nonnegative in all processes (fundamental inequality of dissipation). The generalized forces and fluxes which appear in this expression are functionally related, the state variables occurring in them in the role of parameters. It is shown that the forces or fluxes must appear in a form consisting of two parts. One part is derivable from a potential of dissipation the other part being nondissipative. The paper recalls the linear form of Onsager’s relations and discusses the possibility of their generalization to nonlinear constitutive relations. Even though such a firm generalization does not yet exist, it is possible to discuss two plausible proposals and to examine the relations that link them to each other. The totality of postulates discussed in the paper constitutes a complete thermodynamic formalism. It is shown that Meixner’s fundamental inequality is implied in this formalism and this provides a physical interpretation for his second temperature. Furthermore, the elimination of the internal variables leads to the formalism known as “rational” thermodynamics in which the constitutive relations are given in the form of functionals. This permits us to give a physical interpretation to the concepts of nonequilibrium temperature and entropy considered as “primitive” in “rational” thermodynamics. © Copyright by Walter de Gruyter & Co.