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