Memory effects in glasses: insights into the thermodynamics of out of equilibrium systems revealed by a simple model of the Kovacs effect

TL;DR

This paper uses a simple three-state model to analyze the Kovacs effect in glasses, providing insights into out-of-equilibrium thermodynamics, the concept of fictive temperature, and relaxation phenomena, with implications for education and understanding glassy systems.

Contribution

It introduces a simple, analytically tractable three-state model to study the Kovacs effect and out-of-equilibrium thermodynamics in glasses, extending the concept of fictive temperature.

Findings

The model reproduces the Kovacs hump and asymmetric relaxation.

Fictive temperature is not unique but can be extended to relate to relaxation processes.

The model explains effects like reverse crossover in B2O3 glasses.

Abstract

This paper is an extended version of an article accepted for publication in Physical Review E. Besides its fundamental interest, the model that we investigate in this article is simple enough to be used as a basis for courses or tutorials on the thermodynamics of out of equilibrium systems. It allows simple numerical calculations and analytical analysis which highlight important concepts with an easily workable example. This version includes studies of fast cooling and heating, exhibiting cases with negative heat capacity, and further discussions on the entropy which are not presented in the Physical Review E version. Glasses are interesting materials because they allow us to explore the puzzling properties of out-of-equilibrium systems. One of them is the Kovacs effect in which a glass, brought to an out-of-equilibrium state in which all its thermodynamic variables are identical to those of an equilibrium state, nevertheless evolves, showing a hump in some global variable before the thermodynamic variables come back to their starting point. We show that a simple three-state system is sufficient to study this phenomenon using numerical integrations and exact analytical calculations. It also brings some light on the concept of fictive temperature, often used to extend standard thermodynamics to the out-of-equilibrium properties of glasses. We confirm that the concept of a unique fictive temperature is not valid, an show it can be extended to make a connection with the various relaxation processes in the system. The model also brings further insights on the thermodynamics of out-of-equilibrium systems. Moreover we show that the three-state model is able to describe various effects observed in glasses such as the asymmetric relaxation to equilibrium discussed by Kovacs, or the reverse crossover measured on $B_2O_3$.