The road to equilibrium for a quantum detector resembles a mountain route: the climb is always faster than the descent. An atom accelerated through the vacuum, sensing quantum field fluctuations, heats up to the Unruh temperature. This process is irreversible, but its speed depends on direction: heating outpaces cooling. This asymmetry, known as the quantum Mpemba effect, becomes the key to distinguishing Unruh radiation from ordinary thermal noise.

The Unruh–DeWitt detector is modeled as a two-level atom weakly coupled to a scalar field. Its dynamics are described by the Lindblad equation in the Markovian approximation, and the state is represented by a Bloch vector. The authors compute thermalization trajectories in state space and introduce thermodynamic functions of the process: the rates of change of quantum coherence and heat, which together form a quantum first law. For kinematic analysis, they use metrics from information geometry: Uhlmann fidelity, quantum Fisher information, and quantum degree of completeness.

It is found that during Unruh thermalization, the detector always heats up faster than it cools down for any type of background field: this is a quantum effect similar to the Mpemba effect. This parity dependence is absent in the quantum case and therefore serves as a clear distinguishing feature. Furthermore, the thermalization timescale with a classical bath is significantly longer than with Unruh thermalization.

This work provides a new tool for experimentally testing the Unruh effect: instead of comparing asymptotic spectra, it proposes measuring the dynamics of approach to equilibrium. The asymmetry between heating and cooling, as well as the dependence of the maximum fidelity difference on dimension, are direct consequences of the quantum origin of the radiation and cannot be reproduced by a classical thermal bath. This strengthens the connection between quantum thermodynamics and field physics in curved spacetime.