眼镜中的记忆效应：通过Kovacs效应的简单模型揭示的对非平衡系统热力学的洞察
Memory effects in glasses: insights into the thermodynamics of out of equilibrium systems revealed by a simple model of the Kovacs effect
摘要：
本文是一篇在《物理评论E》上发表的文章的扩展版本。除了它的基本利益，我们在这篇文章中研究的模型是足够简单的，可以用作课程或教程的基础上的热力学平衡系统。它允许简单的数值计算和分析，突出了重要的概念与一个容易操作的例子。这个版本包括快速冷却和加热的研究，展示了负热容的情况，并进一步讨论了物理评论E版中没有的熵。玻璃是一种有趣的材料，因为它们使我们能够探索非平衡系统的令人困惑的性质。其中之一是Kovacs效应，在该效应中，玻璃被带到非平衡态，其中所有的热力学变量与平衡态的热力学变量相同，但是仍然演变，在热力学变量回到其起始点之前，在一些全局变量中显示出驼峰。我们表明，一个简单的三态系统是足够的研究这种现象，使用数值积分和精确的分析计算。它也带来了一些光的概念，虚构的温度，通常用于扩展标准热力学的玻璃的非平衡性质。我们确认，一个独特的虚构温度的概念是无效的，一个显示它可以扩展到与系统中的各种松弛过程的连接。该模型还带来了对非平衡系统热力学的进一步见解。此外，我们表明，三态模型是能够描述的玻璃中观察到的各种效果，如由Kovacs讨论的不对称弛豫平衡，或在$B_2O_3$上测量的反向交叉。
英文摘要：
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 $B_2O_3$.
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