The quantum Mpemba effect (QME) describes the counterintuitive phenomenon in which a system farther from equilibrium reaches the steady state faster than one closer to equilibrium. However, ambiguity in defining a suitable distance measure between quantum states has led to varied interpretations across different contexts. Here we propose the intrinsic quantum Mpemba effect (IQME), defined using the trajectory length traced by the quantum state as a more appropriate measure of distance—distinct from previous trajectory-independent metrics. By treating quantum states as points in a Riemannian space defined by statistical distance, the trajectory length emerges as a more natural and accurate characterization of the counterintuitive dynamics, drawing an analogy to the classical Brachistochrone problem. We demonstrate the existence of IQME in Markovian systems and extend its definition to quantum circuits, thereby establishing a unified framework applicable to both open and closed systems. Notably, we observe an IQME in a U(1)-symmetric circuit, offering insights into the rates of quantum thermalization for different initial states. This work reveals a relatively unexplored nonequilibrium quantum phenomenon, thereby advancing our understanding of quantum state evolution.

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• Open quantum systems & decoherence
• Quantum circuits
• Quantum quench
• Nonequilibrium systems
• Lindblad equation