Operational approach to fluctuations of thermodynamic variables in finite quantum systems

In this paper we present a quantum approach to the old problem of temperature fluctuations. We start by observing that according to quantum thermodynamics, fluctuations of intensive parameters like temperature cannot exist. Furthermore, such parameters are not observables, so their estimation has to be done indirectly. The respective temperature estimate based on quantum measurements of the energy is shown to fluctuate according to the well-known formula Delta T-2 = k(B)T(2)/C, but only within a certain temperature range and if the system is not too small. We also calculate the fourth-order correction term, becoming important at higher temperatures. Finally we illustrate our results with a concrete model of n spins.