The Mpemba effect shows up in quantum operators, not just states

The quantum Mpemba effect — where a system initialized further from equilibrium can paradoxically reach steady state faster — has mostly been studied for quantum states under dissipative dynamics. This work shows the same phenomenon can emerge at the level of operators evolving under the adjoint Liouvillian, the map that governs how observables change in open systems. General conditions for this operator-level Mpemba effect are derived and verified across three distinct open quantum setups. The results suggest a practical handle on controlling how quickly measurable quantities relax in quantum devices.