Planckian bound on quantum dynamical entropy

TL;DR

This paper introduces a simplified quantum dynamical entropy measure, computes its rate in many-body systems, and conjectures a universal Planckian bound on this entropy growth.

Contribution

It presents a new simplified entropy measure for quantum systems and proposes a universal Planckian bound on its entropy rate.

Findings

Explicitly computed entropy rate in thermodynamic and long-time limits.

Demonstrated nonzero entropy growth rate from monitoring thermal fluctuations.

Conjectured a universal Planckian bound for the entropy rate.

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.