Planckian bound on quantum dynamical entropy
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 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.
Cite
@article{arxiv.2507.20914,
title = {Planckian bound on quantum dynamical entropy},
author = {Xiangyu Cao},
journal= {arXiv preprint arXiv:2507.20914},
year = {2026}
}
Comments
13 pages, 3 figures; v4: reorganised presentation, added discussion on experimental accessibility; v3: new results, improved presentation, extended appendix; v2: minor change, updated references