Thermalization and Mpemba-like patterns in effective temperature dynamics of strongly coupled dissipative quantum chaotic systems

Abstract

Anomalous thermalization, particularly the crossings of temperature trajectories from different initial states termed Mpemba crossings (MPCs), have intrigued scientists for decades. While recent studies in quantum systems suggest that initial conditions play a decisive role in its emergence, they offer limited insight into MPCs in complex, highly nonequilibrium systems. In this study, we investigate temperature dynamics in the strongly coupled, quantum chaotic Sachdev-Ye-Kitaev (SYK) model, which is dual to the low-energy dynamics of 2D dilaton gravity. Our findings reveal a dynamically driven nonequilibrium mechanism underlying MPCs during rapid thermalization, with implications for gravitational systems. We explore quench dynamics in SYK systems under three conditions: coupling to a single SYK thermal bath, coupling to two thermal baths at different temperatures, and dissipative SYKs modeled by the Lindblad equation. We find that strong system-bath coupling induces oscillating effective temperatures and trajectory crossings in transient states due to nonequilibrium statistics, phenomena absent in quasi-static thermodynamics and Lindbladian SYKs. These MPCs highlight a unique feature of anomalous thermalization of strongly coupled quantum chaotic systems driven far from equilibrium. Besides, the results also provide qualitative insights into the nonequilibrium thermodynamics of black holes strongly interacting with their environment, such as primordial black holes in the early universe.