Anomaly to Resource: The Mpemba Effect in Quantum Thermometry

Quantum thermometry provides a key capability for nanoscale devices and quantum technologies, but most existing strategies rely on probes initialized near equilibrium. This equilibrium paradigm imposes intrinsic limitations: sensitivity is tied to long-time thermalization and often cannot be improved in fast, noisy, or nonstationary settings. In contrast, the Mpemba effect, the counterintuitive phenomenon where hotter states relax faster than colder ones, has mostly been viewed as a thermodynamic anomaly. Here, we bridge this gap by proving that Mpemba-type inversions generically yield a finite-time enhancement of the quantum Fisher information (QFI) for temperature estimation, thereby converting an anomalous relaxation effect into a concrete metrological resource. Through explicit analyses of two-level and Λ-level probes coupled to bosonic baths, we show that nonequilibrium initializations can transiently outperform both equilibrium strategies and colder states, realizing a metrological Mpemba effect. Our results establish anomalous relaxation as a general design principle for nonequilibrium quantum thermometry, enabling ultrafast and nanoscale sensing protocols that exploit, rather than avoid, transient dynamics.