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

TL;DR

This paper develops a thermodynamic framework for amorphous materials focusing on internal degrees of freedom, specifically vacancies, to understand volume changes and their dynamics through both thermodynamic and statistical approaches.

Contribution

It introduces a combined thermodynamic and statistical approach to model internal vacancy dynamics and volume deformation in amorphous materials, deriving detailed equations of motion.

Findings

Vacancies govern irreversible volume changes.

Deformation enhances rate factors via noisy fluctuations.

Thermodynamic and statistical analyses are consistent and complementary.

Abstract

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.