Geometry and restoration of the quantum Mpemba effect beyond weak-coupling regime in the spin-boson model

Understanding relaxation dynamics in open quantum systems is a central problem in nonequilibrium quantum physics. Here we investigate the quantum Mpemba effect in the spin-boson model. In the weak-coupling Markovian regime we show that the occurrence of the effect strongly depends on the choice of distance measure at low temperature: while it appears in the trace distance, it can disappear in the quantum relative entropy. Going beyond the weak-coupling approximation, numerically exact simulations of the full system-bath dynamics reveal that increasing coupling enhances the effect in the trace distance and restores it in the quantum relative entropy. For all spin-bath couplings prior to delocalized-localized quantum phase transition, we uncover a simple geometric structure of the effect on the Bloch sphere: within the excited-state hemisphere, pairs of states related by rotations generically exhibit relaxation-order inversion. These results highlight the role of geometry and system-environment correlations in anomalous quantum relaxation.