15 November 2022 Tue 4 pm

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The notion of thermodynamic entropy in the context of quantum mechanics is a controversial topic. While there were proposals to refer von Neumann entropy as thermodynamic entropy, it has its own limitations. In the past few years, 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 thermodynamic entropy in quantum mechanics. In this work, we study the behavior of the observational entropy in the context of localization-delocalization transition for the 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.

Ref:  R Modak and S Aravinda arXiv:2209.10273 (2022)

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