Scrambling Enabled Entropy Accumulation in Open Quantum Systems

In closed quantum many-body systems, initially localized information spreads throughout the system and becomes highly complex. This phenomenon, known as information scrambling, is closely related to entropy growth and quantum thermalization. Recent studies have shown that dissipation in open systems can hinder information scrambling, driving the system into a dissipative phase when the system-bath coupling is strong. However, the signature of this scrambling transition in entropy dynamics remains unexplored. In this work, we unveil a novel phenomenon in open quantum systems, termed entropy accumulation, which occurs exclusively within the scrambling phase. We consider a setup in which a probe is weakly coupled to a system that is already interacting with a bath. We calculate the increase in the second R\'enyi entropy induced by an external impulse on the system, after tracing out the probe. Despite the system-probe coupling being weak, the entropy continues to increase and eventually saturates at a finite value due to operator growth. In contrast, the entropy increase is limited by the coupling strength in the dissipative phase. The theoretical prediction is derived from both general arguments and an explicit example using generalized Boltzmann equations. Our results offer new insights into the intriguing relationship between entropy dynamics and information scrambling in open quantum systems.