Page Curve from Non-Markovianity

TL;DR

This paper uses the Sachdev-Ye-Kitaev model to demonstrate how non-Markovian environments can produce a Page curve in entropy dynamics, showing initial growth, a peak, and subsequent decrease, revealing universal features of chaotic quantum systems.

Contribution

It provides an exact solution showing how non-Markovian effects lead to a Page curve in entropy, extending understanding of entropy dynamics in chaotic quantum systems.

Findings

Initial entropy increases linearly, matching Markovian results.

Long-time entropy can decrease due to non-Markovian effects.

Universal applicability to chaotic quantum many-body systems.

Abstract

In this letter, we use the exactly solvable Sachdev-Ye-Kitaev model to address the issue of entropy dynamics when an interacting quantum system is coupled to a non-Markovian environment. We find that at the initial stage, the entropy always increases linearly matching the Markovian result. When the system thermalizes with the environment at a sufficiently long time, if the environment temperature is low and the coupling between system and environment is weak, then the total thermal entropy is low and the entanglement between system and environment is also weak, which yields a small system entropy in the long-time steady state. This manifestation of non-Markovian effects of the environment forces the entropy to decrease in the later stage, which yields the Page curve for the entropy dynamics. We argue that this physical scenario revealed by the exact solution of the Sachdev-Ye-Kitaev model is universally applicable for general chaotic quantum many-body systems and can be verified experimentally in near future.