Mathematical expressions for quantum fluctuations of energy for different energy-momentum tensors.

Expressions for the quantum fluctuations of energy density have been derived for the subsystems consisting of hot relativistic gas of particles with spin-$\frac{1}{2}$ and mass $m$. Our expressions for the fluctuation depend on the form of energy-momentum tensor which is because of the dependence of the latter on the pseudo-gauge. These results suggest that quantum fluctuations of energy should be considered seriously in case of very small thermodynamic systems.