Irreversible Thermodynamics and Rate Theory.

Introduction.-The "classical theory of irreversible thermodynamics"1 may be said to have its origin in the formulation of the "reciprocity relations" by Onsager.2 The basis of this theory may be summarized briefly as follows (for a complete discussion see works cited in ref. 1 and 2): in the limit of small excursions from thermodynamic equilibrium, changes in the properties of any system are described by certain formalized force8 and fluxe8. In general, the flux of any property (e.g., matter, heat, electricity, etc.) may be taken as linearly dependent upon all the forces (concentration or temperature gradients, potential differences, etc.). If, in this set of linear equations-called the "phenomenological equations"-the forces and fluxes are properly defined, the coefficient Li1 of the jth force in the equation for the ith flux must, according to the "reciprocity relations," equal the coefficient Lit, defined in the same manner. The correct choice of these forces and fluxes is determined by the condition that the time rate of change of the entropy of the system be given by the sum over the products of each force by its corresponding flux. The application of this treatment to processes involving simultaneous gradients of temperature, concentration, chemical potential, or electrical potential has been uniformly successful, provided only that the gradients are sufficiently small, i.e., the system is nearly at equilibrium. Exactly how near the equilibrium state the system must be, however, in order that the postulated linearity will suffice as an adequate approximation is not always made clear; for most purely physical phenomena of this type, as, for example, Thompson and Peltier heats, it appears that the formulation is adequate under nearly all experimental conditions. In diffusion and chemical reaction, on the other hand, the several approximations described above are almost never satisfactory in cases of practical interest, and the deductions of this type of theory become, to a large extent, only academically interesting. It would appear that in these cases, at least, a higher degree of approximation in relating the forces and fluxes of a given system is required. Unfortunately, any attempt in this direction requires that the linear relation between forces and fluxes, and hence the symmetry properties of the matrix of phenomenological coefficients (the Onsager conditions), be given up, and the whole approach becomes impractically cumbersome. An additional problem arises from the fact that, strictly speaking, thermodynamic variables such as entropy which appear in the algebraic formulation are not well defined except at thermodynamic equilibrium, and their precise meaning becomes less clear the further the system deviates from this state. Any attempt to describe a nonequilibrium system in terms of purely thermodynamic variables must suffer from this logical difficulty, and it is not immediately apparent that there exists any way in which this conflict can be resolved within the framework of the classical theory of continuum thermohydrodynamics. On the other hand, there is quite general treatment of irreversible procsses based