  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.
