Planckian bound on quantum dynamical entropy
Xiangyu Cao (LPENS, Paris)
Kolmogorov and Sinai’s dynamical entropy is a quantitative diagnosis of classical chaos. However its quantum generalisations, developed by mathematical physicists around 1990, have been overlooked by the recent literature on many-body quantum chaos. After a gentle background review, I will explain Connes-Narnhofer-Thirring’s quantum dynamical entropy (simplified) in terms of monitored quantum dynamics. I will show that the entropy rate can be nonzero, and exactly calculable, in many-body systems away from semiclassical/large N limits, and arguably satisfy a Planckian bound, akin to that of Maldacena-Shenker-Stanford on out of time correlators. Time permitting I will discuss other quantum dynamical entropies and/or related questions on decoherent histories in many-body systems. Based on 2507.20914 and 2603.15753.