Non-Markovianity in Chaotic Many-body Systems

The process tensor captures how an environment influences a system across multiple time intervals, and its multi-time mutual information furnishes a measure of non-Markovianity. We examine the non-Markovianity of a subsystem's dynamics embedded in various unitary evolutions of the global system, described by random matrices, various Sachdev-Ye-Kitaev models, and holographic conformal field theories. This non-Markovianity arises from two distinct mechanisms: (i) interaction-induced temporal correlations, which appear already at early times, and (ii) entanglement phase transition, which appears at the Page time of a finite environment. We further show that the process-tensor mutual information coincides with the timeline pseudo-entropy when the subsystem is depolarized and establishes its holographic correspondence in the dual black hole spacetime. Our results on non-Markovianity connect the fields of quantum chaos, many-body dynamics, and the black hole information problem.