Quantum thermometry aims to measure temperature in nanoscale quantum systems, paralleling classical thermometry. Nonequilibrium quantum thermometry, emerging as a complement to its equilibrium counterpart, addresses scenarios where thermalization is prohibitively slow or real-time temperature monitoring is required. Since temperature is not well defined for nonequilibrium states, a direct inference of temperature values might seem impossible in nonequilibrium quantum thermometry, unlike in the thermal equilibrium case. Here we show that direct temperature inference from the nonequilibrium dynamics of a thermometer is achievable by developing a thermodynamic inference scheme. The scheme integrates two conceptual developments. (i) By applying the maximum-entropy principle with the thermometer's mean energy as a constraint, we assign a reference temperature to the nonequilibrium thermometer. We demonstrate that this reference temperature outperforms a commonly used effective temperature defined through equilibrium analogy. (ii) We obtain positive-semidefinite error functions that lower bound the deviation of the reference temperature from the true temperature and vanish upon thermalization with the sample. Combining the reference temperature with these error functions, we introduce a notion of corrected dynamical temperature which furnishes a postprocessed temperature inference under nonequilibrium conditions. This corrected dynamical temperature can be evaluated adaptively without prior knowledge of the actual temperature. We validate the corrected dynamical temperature in a qubit-based thermometer under a range of nonequilibrium initial states, confirming its capability to estimate the true temperature. Importantly, we find that increasing quantum coherence can enhance the precision of this readout. Our findings complement existing research on nonequilibrium quantum thermometry and help bridge the gap between prevailing theoretical analysis on precision limit and the practical need of direct temperature inference.

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• Quantum thermodynamics
• Nonequilibrium systems
• Master equation