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This is the first of three papers devoted to the nonequilibriumthermodynamics of amorphous materials. Our focus here is on the role ofinternal degrees of freedom in determining the dynamics of such systems. Forillustrative purposes, we study a solid whose internal degrees of freedom arevacancies that govern irreversible volume changes. Using this model, we comparea thermodynamic theory based on the Clausius-Duhem inequality to a statisticalanalysis based directly on the law of increase of entropy. The statisticaltheory is used first to derive the the Clausius-Duhem inequality. We then usethe theory to go beyond those results and obtain detailed equations of motion,including a rate factor that is enhanced by deformation-induced noisyfluctuations. The statistical analysis points to the need for understanding howboth energy and entropy are shared by the vacancies and their environments.

Nonequilibrium Thermodynamics of Amorphous Materials I: Internal Degrees of Freedom and Volume Deformation