Thermodynamics emerged as a phenomenological theory boosted by the need to control and enhance the performances of the newly invented steamengines during the industrial revolution.

The recent achievements of modern nanotechnologies introduced the necessity to control the system at lenghscales where quantum effects need to be taken into account. In this context the measurement of temperature plays a fundamental role.

Modern physics addresses these problems by feeding them into mindset of statistical mechanics, which tackles the average properties of physical systems by smoothing out the local details. This description is no more applicable when technical or practical limitations restrict our capabilities of observing the system to local probing. For example, the fact that the ultimate precision limit to temperature estimation via global measurements is related to the heat capacity of the system, is no longer guaranteed at a local microscopic level.

In a research just published in Nature Communications, Antonella De Pasquale, Davide Rossini, Rosario Fazio and Vittorio Giovannetti fill this gap. They propose a quantum-metrology approach to thermodynamics. In the specific the authors introduce a sort of mesoscopic version of the heat capacity which rigorously quantifies the highest achievable accuracy for estimating the temperature
of a quantum system at thermal equilibrium solely through local measurements.

The results arising from these studies could be exploited in the development of quantum thermal machines, where a robust level of control is required, or in other contexts related for instance to biology and medicine.