Quantum Mpemba-like effect in Unruh thermalization

Abstract

We revisit the thermal nature of the Unruh effect within a quantum thermodynamic framework. For a Unruh-deWitt (UDW) detector in $n$-dimensional Minkowski spacetime, we demonstrate that its irreversible thermalization to a Gibbs equilibrium state follows distinct trajectories on the Bloch sphere, which depend on the types of fields the detector interacts with, as well as the spacetime dimensionality. Using thermodynamic process functions, particularly quantum coherence and heat that form the quantum First Law, we characterize the Unruh thermalization through a complementary time evolution between the trajectory-dependent rates of process functions. Grounded in information geometry, we further explore the kinematics of the detector state as it "flows" along the trajectory. In particular, we propose two heating/cooling protocols for the UDW detector undergoing Unruh thermalization. We observe a quantum Mpemba-like effect, characterized by faster heating than cooling in terms of Uhlmann fidelity "distance" change. Most significantly, we establish the maximum fidelity difference as a novel diagnostic that essentially distinguishes between Unruh thermalization and its classical counterpart, i.e., classical thermal bath-driven thermalization of an inertial UDW detector. This compelling criterion may serve as a hallmark of the quantum origin of the Unruh effect in future experimental detection and quantum simulation. Finally, we conclude with a general analysis of Unruh thermalization, starting from equal-fidelity non-thermal states, and demonstrate that the detectors' fidelity and "speed" of quantum evolution still exhibit a Mpemba-like behavior.