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arXiv · 2507.20914

Planckian bound on quantum dynamical entropy

Xiangyu Cao
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Abstract

We introduce a simplified version of Connes-Narnhofer-Thirring's quantum dynamical entropy for quantum systems. It quantifies the amount of information gained about the initial condition from continuously monitoring an observable. A nonzero entropy growth rate can be obtained by monitoring the thermal fluctuation of an extensive observable in a generic many-body system, away from classical or large $N$ limits. We explicitly compute the entropy rate in the thermodynamic and long-time limit, in terms of the two-point correlation functions. We conjecture a universal Planckian bound for the entropy rate. Related results on the purification rate are also obtained.

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Xiangyu Cao. 2025-07-28. Planckian bound on quantum dynamical entropy. https://doi.org/10.1103/wd91-v58h

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