The notion of the thermodynamic entropy in the context of quantum mechanics is a controversial topic. While there were proposals to refer von Neumann entropy as the thermodynamic entropy, but it has it's own limitations. In the past few years, the observational entropy has been developed as a generalization of Boltzmann entropy to quantum mechanics, and it is presently one of the most promising candidates to provide a clear and well-defined understanding of the thermodynamic entropy in quantum mechanics. In this work, we study the behaviour of the observational entropy in the context of localization-delocalization transition for one-dimensional Aubrey-Andre (AA) model. We find that for the typical mid-spectrum states, in the delocalized phase the observation entropy grows rapidly with coarse-grain size and saturates to the maximal value, while in the localized phase the growth is logarithmic. Moreover, for a given coarse-graining, it increases logarithmically with system size in the delocalized phase, and obeys area law in the localized phase. We also find the increase of the observational entropy followed by the quantum quench, is logarithmic in time in the delocalized phase as well as at the transition point, while in the localized phase it oscillates.

中文翻译：

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安德森定位的观测熵研究

在量子力学的背景下，热力学熵的概念是一个有争议的话题。虽然有人提议将冯诺依曼熵称为热力学熵，但它有其自身的局限性。在过去的几年里，观测熵已经发展为将玻尔兹曼熵推广到量子力学，它是目前最有希望提供对量子力学中热力学熵的清晰和明确理解的候选方法之一。在这项工作中，我们研究了一维 Aubrey-Andre (AA) 模型在定位-离域转换背景下的观测熵行为。我们发现对于典型的中谱状态，在离域阶段，观测熵随着粗粒度快速增长并饱和到最大值，而在局部阶段，增长是对数的。此外，对于给定的粗粒度，它在离域阶段随系统大小成对数增加，在局部阶段服从面积定律。我们还发现观察熵的增加随后是量子猝灭，在离域相和过渡点的时间上是对数的，而在局部相它是振荡的。