The quantum Mpemba effect occurs when a quantum system, residing far away from the steady state, relaxes faster than a relatively nearer state. We look for the presence of this highly counterintuitive effect in the relaxation dynamics of the operators within the open quantum system setting. Since the operators evolve under a nontrace preserving map, the trace distance of an operator is not a monotonically decaying function of time, unlike its quantum state counterpart. Consequently, the trace distance cannot serve as a reliable measure for detecting the Mpemba effect in operator dynamics. We circumvent this problem by defining a dressed distance between operators that decays monotonically with time, enabling a generalized framework to explore the Mpemba-like effect for operators. Applying the formalism to various open quantum system settings, we find that, interestingly, in the single qubit with Davies-type thermalizing model, only accelerated relaxation of operators is possible, while genuine Mpemba-like effects emerge in higher-dimensional systems such as qutrits and beyond. Furthermore, we demonstrate the existence of Mpemba-like effects in nonlocal, nonequilibrium operators, such as current, in a double-quantum-dot setup. Our results, in addition to offering fundamental insight about the occurrence of the Mpemba-like effect under non-trace-preserving dynamics, open avenues for experimental studies where quicker relaxation of observables could be of significant interest.

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• Open quantum systems & decoherence
• Quantum thermodynamics