Bridging thermodynamics and metrology in non-equilibrium Quantum Thermometry

Single-qubit thermometry presents the simplest tool to measure the temperature of thermal baths with reduced invasivity. At thermal equilibrium, the temperature uncertainty is linked to the heat capacity of the qubit, however the best precision is achieved outside equilibrium condition. Here, we discuss a way to generalize this relation in a non-equilibrium regime, taking into account purely quantum effects such as coherence. We support our findings with an experimental photonic simulation.