Nonequilibrium Thermodynamics of the Kovacs Effect

TL;DR

This paper develops a thermodynamic framework for understanding the Kovacs effect in glasses, emphasizing the role of an effective temperature and internal variables in out-of-equilibrium relaxation processes.

Contribution

It introduces a new thermodynamic theory linking configurational degrees of freedom, effective temperature, and internal variables to explain the Kovacs effect.

Findings

Identifies two mechanisms for internal variable relaxation.

Explains how irreversible dynamics affect entropy and effective temperature.

Interprets numerical simulations of the Kovacs effect using the theory.

Abstract

We present a thermodynamic theory of the Kovacs effect based on the idea that the configurational degrees of freedom of a glass-forming material are driven out of equilibrium with the heat bath by irreversible thermal contraction and expansion. We assume that the slowly varying configurational subsystem, i.e. the part of the system that is described by inherent structures, is characterized by an effective temperature, and contains a volume-related internal variable. We examine mechanisms by which irreversible dynamics of the fast, kinetic-vibrational degrees of freedom can cause the entropy and the effective temperature of the configurational subsystem to increase during sufficiently rapid changes in the bath temperature. We then use this theory to interpret the numerical simulations by Mossa and Sciortino (MS), who observe the Kovacs effect in more detail than is feasible in laboratory experiments. Our analysis highlights two mechanisms for the equilibration of internal variables. In one of these, an internal variable first relaxes toward a state of quasi-equilibrium determined by the effective temperature, and then approaches true thermodynamic equilibrium as the effective temperature slowly relaxes toward the bath temperature. In the other mechanism, an internal variable directly equilibrates with the bath temperature on intermediate timescales, without equilibrating with the effective temperature at any stage. Both mechanisms appear to be essential for understanding the MS results.