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 ${\text{B}}_2{\text{O}}_3$.

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眼镜中的记忆效应：通过简单的科瓦奇效应模型揭示失衡系统的热力学

眼镜是有趣的材料，因为它们使我们能够探索不平衡系统的令人困惑的特性。其中之一是科瓦茨效应，其中玻璃进入非平衡状态，其中其所有热力学变量与平衡状态相同，但仍在演化，在热力​​学变量之前，某些全局变量出现了驼峰。回到他们的起点。我们表明，简单的三态系统足以使用数值积分和精确的分析计算来研究此现象。它也为虚拟温度的概念提供了一些启示，通常用于将标准热力学扩展到玻璃的失衡特性。我们确认唯一虚拟温度的概念无效，可以扩展它以与系统中的各种放松过程建立联系。该模型还为失衡系统的热力学带来了进一步的见解。此外，我们表明三态模型能够描述在玻璃中观察到的各种效应，例如由Kovacs讨论的不对称松弛到平衡，或在${\text{乙}}_2{\text{Ø}}_3$。