The Mpemba Paradox: Hot Quantum Sensors Measure Temperature More Accurately express
A cook sprays water onto a hot skillet: droplets sizzle and vanish, instantly signaling the temperature — faster than waiting for a thermometer. A similar principle now works in quantum thermometry. A tiny sensor (say, an atom) is deliberately heated, and as it rushes back toward rest, the growth of entropy (disorder) as per Boltzmann’s legacy, it briefly becomes hypersensitive to the ambient temperature. The paradox: starting from a hot state accelerates cooling — exactly like the Mpemba effect, where hot water freezes faster than cold.
This is critical for quantum computers and microchips, where conventional thermal control is impossible. And the Mpemba effect itself still lacks a single explanation — scientists still debate the causes, yet it already serves as a practical tool.
Original abstract
as written by the authors arXiv:2601.05046
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 \textit{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 $$\Lambda$$-level probes coupled to bosonic baths, we show that nonequilibrium initializations can transiently outperform both equilibrium strategies and colder states, realizing a \emph{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.
The Mpemba effect remains a mystery: scientists cannot unequivocally explain it. Hypotheses include evaporation, convection, and supercooling.