Tunable quantum Mpemba effect in a three-terminal double quantum-dot system with photon-assisted transport

Abstract The Mpemba effect describes a counterintuitive relaxation phenomenon where a system initially farther from equilibrium reaches the steady state faster than one initially closer. Using the non-equilibrium free energy as a thermodynamic measure to quantify the distance from equilibrium, we investigate this effect in an inelastic three-terminal double quantum dot system coupled to a photon reservoir. By engineering initial states that minimize overlap with the slowest decaying eigenmode, we demonstrate that under appropriate parameters a mixed state, despite being initially farther from equilibrium, can relax more rapidly than a pure state, revealing a clear Mpemba effect in this system. We further show that inelastic electron-photon interactions can tune the relaxation spectrum, providing a pathway to resonantly enhance this anomalous relaxation, while quantum coherence exhibits a dual role, either facilitating or hindering the effect depending on the parameter regime. Our results connect the Mpemba effect to decay mode engineering, inelastic transport, and coherence control, extending the understanding of anomalous relaxation in open quantum systems.