Non-Markovian entropy production and its connection to global entanglement in quantum chaos

We focus on the problem of identifying dynamical signatures of quantum behavior, particularly quantum chaos. Recently, we proposed a method for efficiently computing the dynamics of an open quantum system, based on emergent integrals of motion that dynamically form in the environment after a local quench. These integrals carry away the system's entanglement entropy.
We show that in the Markovian limit, resembling ancilla-based models, entropy production grows linearly and integrable and chaotic behavior are indistinguishable. In contrast, in the non-Markovian regime, entropy production closely follows the Meyer–Wallach global entanglement measure and serves as a sensitive probe of quantum chaos. Thus, we propose non-Markovian entropy production as a marker of quantum chaos.