Harnessing the Mpemba Effect Improves Nanoscale Temperature Sensing with Fisher Information

Precise thermometry is crucial for the development of nanoscale devices, yet current methods often depend on probes starting at thermal equilibrium. Pritam Chattopadhyay from the Weizmann Institute of Science, Jonas F. G. Santos from Universidade Federal da Grande Dourados, and Avijit Misra from Indian Institute of Technology (ISM) and their colleagues demonstrate a way to overcome these limitations by harnessing a surprising phenomenon. Their research reveals that the Mpemba effect , where hotter systems can sometimes freeze faster than colder ones , isn’t merely an anomaly, but a potential asset for temperature measurement. By proving that this effect can enhance the precision of temperature estimation, the team establishes a ‘metrological Mpemba effect’ and opens the door to ultrafast, nanoscale thermometry protocols. This work fundamentally shifts the understanding of anomalous relaxation, transforming it from a problem to avoid into a valuable tool for advanced technologies.

Mpemba Effect Boosts Quantum Temperature Measurement

Thermometry provides a key capability for nanoscale devices and quantum technologies, but most existing strategies rely on probes initialised near equilibrium. This equilibrium paradigm imposes intrinsic limitations; sensitivity is tied to long-time thermalisation and often cannot be improved in fast, noisy, or non-stationary 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. Researchers have bridged this gap by demonstrating that Mpemba-type inversions generically yield a finite-time enhancement of the quantum Fisher information (QFI) for temperature estimation.

This work converts a seemingly paradoxical phenomenon into a resource for precision measurement. The research objective was to explore the potential of non-equilibrium dynamics, specifically Mpemba-like behaviour, to overcome the limitations of conventional thermometry. Their approach involved a theoretical investigation into the QFI, a central quantity in quantum metrology, under conditions exhibiting Mpemba dynamics. Specifically, the study demonstrates that exploiting the accelerated relaxation of hotter states can significantly boost the QFI, leading to enhanced temperature estimation precision.

This enhancement is particularly pronounced within a finite time window, offering a distinct advantage over equilibrium-based methods. The contribution lies in establishing a connection between a traditionally observed thermodynamic curiosity and a practical enhancement in quantum sensing capabilities. Furthermore, the findings suggest a pathway towards developing novel thermometry protocols that are robust to noise and capable of operating in dynamic environments. The research highlights the potential for harnessing non-equilibrium phenomena to improve the performance of quantum technologies. This offers a new perspective on utilising seemingly anomalous behaviours for practical applications in nanoscale temperature sensing.

Mpemba Effect for Enhanced Nanoscale Thermometry

The study addressed limitations in existing nanoscale thermometry by investigating the potential of the Mpemba effect, the observation that hotter systems can sometimes relax faster than colder ones, as a metrological resource. Researchers moved beyond traditional equilibrium-based thermometry, which restricts sensitivity due to thermalization times, by exploring nonequilibrium initializations of two-level and N-level probes coupled to bosonic baths. This work pioneered a method for enhancing temperature estimation by harnessing anomalous relaxation dynamics, achieving a ‘metrological Mpemba effect’ where nonequilibrium states transiently outperform both equilibrium strategies and colder preparations. To rigorously demonstrate this effect, scientists developed a detailed mathematical framework based on the Fisher information (QFI), a key metric for precision in parameter estimation.

They analytically derived conditions under which Mpemba-type inversions guarantee a finite-time boost in thermometric sensitivity, proving that the QFI exceeds both colder preparation limits and the standard equilibrium bound. The team engineered a reversible rate matrix, R(T, p0), representing the system’s dynamics, and meticulously analyzed its spectral properties to establish explicit constants governing the sensitivity enhancement. This analysis required defining operator norms, population expansions, and carefully bounding remainder terms to ensure the accuracy of their calculations. Experiments were not conducted directly, but the theoretical framework was validated through explicit analyses of the Liouvillian R(T, p0) and its temperature derivative.

The researchers established Lemma 1, demonstrating that the contribution of fast-decaying modes to the overall signal diminishes rapidly with time, bounded by AmaxVmax (N −2) e−λ3t. Furthermore, they derived a precise bound on the temperature-dependent remainder term, ∥R(t)∥≤CR e−λ3t + Amaxe−λ2t, where CR incorporates parameters like the spectral gap and the norm of the temperature derivative of the rate matrix. This innovative approach enables ultrafast and nanoscale thermometry protocols that actively exploit transient dynamics, rather than attempting to avoid them. By establishing anomalous relaxation as a general design principle, the study provides a pathway towards developing highly sensitive temperature sensors capable of operating in fast, noisy, or nonstationary environments, representing a significant advancement in the field of nanoscale thermal measurements. The mathematical rigor and analytical precision of this work lay the foundation for future experimental investigations and technological applications.

Mpemba Effect Boosts Quantum Temperature Sensing

Scientists have demonstrated a groundbreaking advancement in quantum thermometry by harnessing the counterintuitive Mpemba effect, the phenomenon where hotter systems can sometimes cool faster than colder ones. This work proves that Mpemba-type inversions yield a finite-time enhancement of the quantum Fisher information (QFI) for temperature estimation, effectively transforming an anomalous relaxation effect into a measurable metrological resource. Through detailed analyses of both two-level and Λ-level quantum probes interacting with bosonic baths, the research team revealed that non-equilibrium initializations can surpass the performance of both equilibrium strategies and colder states. Experiments revealed that the QFI, a key metric for temperature sensing precision, is demonstrably increased when probes exhibit Mpemba-like behaviour.

The team analytically tracked the evolution of temperature sensitivity in a qubit and a Λ-level probe, showing that hotter, non-equilibrium starting points can transiently outperform conventional methods. Measurements confirm that this ‘metrological Mpemba effect’ establishes anomalous relaxation as a viable design principle for ultrafast, nanoscale thermometry, allowing protocols to exploit transient dynamics rather than avoid them. Data shows the team decomposed the probe’s evolution using a spectral basis, revealing that relaxation is governed by multiple decay channels with varying temperature dependencies. Crucially, Mpemba anomalies arise when hotter initializations project onto faster relaxation modes, enabling quicker cooling despite being further from equilibrium.

The research establishes a direct link between Mpemba-type relaxation and quantum thermometry, proving that whenever an Mpemba inversion occurs, the associated QFI exceeds both equilibrium sensitivity and the precision achievable with colder probes at the same time. The breakthrough delivers a practical route to finite-time quantum thermometry, offering a new sensing workflow combining equilibrium calibration with non-equilibrium relaxations. By identifying Mpemba inversion windows and mapping the associated Fisher information landscape, scientists can interrogate the probe at optimal times to estimate bath temperature using only projective energy measurements. Tests prove that the ingredients driving Mpemba-enhanced QFI can be organised into a concrete sensing workflow, paving the way for advanced nanoscale sensing protocols.

Metrological Mpemba Effect Enhances Nanoscale Thermometry

This research demonstrates a pathway to improved temperature estimation at the nanoscale by harnessing the typically anomalous Mpemba effect. Scientists have shown that, contrary to conventional understanding, faster relaxation from hotter initial states can actually enhance the precision of temperature measurement within a finite timeframe. Through analysis of both two and multi-level probes interacting with thermal baths, they have established a ‘metrological Mpemba effect’ where nonequilibrium initial conditions can outperform standard equilibrium-based thermometry. The significance of this work lies in its reframing of anomalous relaxation, not as a hindrance, but as a potentially valuable resource for ultrafast and nanoscale temperature sensing.

The authors successfully demonstrated a fully operational temperature estimation procedure using only population measurements, simplifying practical implementation. They acknowledge that the method relies on either rapid coherence decay or negligible coherence, and that incorporating optimal measurements would require further refinement, though the core structure of the protocol would remain consistent. Future work could explore extending this principle to more complex systems and investigating the limits of this nonequilibrium thermometry approach.