Pseudogauge dependence of quantum fluctuations of the energy in a hot relativistic gas of fermions

Explicit expressions for quantum fluctuations of energy in subsystems of a hot relativistic gas of spin-1/2 particles are derived. The results depend on the form of the energy-momentum tensor used in the calculations, which is a feature described as pseudogauge dependence. However, for sufficiently large subsystems the results obtained in different pseudogauges converge and agree with the canonical-ensemble formula known from statistical physics. As different forms of the energy-momentum tensor of a gas are a priori equivalent, our finding suggests that the concept of quantum fluctuations of energy in very small thermodynamic systems is pseudogauge dependent. On the practical side, the results of our calculations determine a scale of coarse graining for which the choice of the pseudogauge becomes irrelevant.