Thermodynamics of internal variables in the context of the absolute reaction rate theory

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Abstract
In this paper we present a nonlinear internal constitutive equation which we have obtained by unifying the theory of ’’The Thermodynamics of Internal Variables’’ and a modified version, presented here, of ’’The Theory of Absolute Reaction Rates’’. The chief characteristic of this equation is the explicit form of the nonlinear relation between the internal forces and the rates of change of the internal variables. In addition, we have given the internal variables a precise physical interpretation. An internal variable in effect represents the average displacement of a group of atoms whose motion is impeded by a potential energy barrier of a specific height. As a consequence, the microforce encountered in the Eyring theory is identified as the free energy gradient causing the displacement of this particular group; the precise relationship between the microforce and the externally applied force field is also established. It is deduced that the single‐well model, characteristic of theories with one internal variable, represents the mechanical response of a p e r f e c t crystal to externally applied force fields. The theory developed, herein, is anticipated to have wide applicability in the mathematical representation of the rate dependent behavior of metals and other materials.

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