Planckian bound on quantum dynamical entropy
arXiv:2507.20914 · doi:10.1103/wd91-v58h
The paper defines a simplified quantum dynamical entropy that measures information gained by continuously monitoring an observable, computes its growth rate for generic many‑body systems using correlation functions, and proposes a universal Planckian bound on that rate, also discussing related purification dynamics.
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.
13 pages, 3 figures; v5: minor typo fixes, matching published version; v4: reorganised presentation, added discussion on experimental accessibility; v3: new results, improved presentation, extended appendix; v2: minor change, updated references