Quantum Mpemba Effect in a Four‐Site Bose–Hubbard Model

ABSTRACT We investigate relaxation‐order inversion, known as the quantum Mpemba effect (QME), in a minimal open many‐body system called a one‐dimensional four‐site Bose–Hubbard chain governed by Lindblad dynamics with local number dephasing. Families of thermal initial states are prepared at a fixed temperature and evolved under a common reference Liouvillian toward the same stationary state. Relaxation is characterized using four complementary diagnostics: trace distance, quantum relative entropy, symmetry‐projected entropy imbalance (entanglement asymmetry), and the ‐norm of coherence in the Fock basis. We find that QME emerges robustly in ‐the clean interacting regime, where on‐site interactions redistribute the overlaps of initial states with slow Liouvillian decay modes, enabling states initially farther from equilibrium to converge faster at late times. In contrast, the noninteracting limit exhibits a monotonic relaxation hierarchy across all metrics. Introducing a linear Stark potential or random on‐site disorder suppresses relaxation and eliminates QME signatures by inhibiting transport‐assisted mixing and enhancing the dominance of slow modes. Within the explored parameter regime, the Stark field induces significantly stronger retardation than disorder. We further show that symmetry‐projected entropy imbalance is particularly sensitive to charge‐sector decoherence in reduced subsystems and provides a stringent probe of QME in bosonic platforms. Our results elucidate the essential role of interactions in enabling anomalous relaxation in open lattice systems and connect the suppression of QME under spatial inhomogeneity to localization phenomena in tilted and disordered Bose–Hubbard chains.