  We derive a formula that defines quantum fluctuations of energy in subsystems
of a hot relativistic gas. For small subsystem sizes we find substantial
increase of fluctuations compared to those known from standard thermodynamic
considerations. However, if the size of the subsystem is sufficiently large, we
reproduce the result for energy fluctuations in the canonical ensemble. Our
results are subsequently used in the context of relativistic heavy-ion
collisions to introduce limitations of the concepts such as classical energy
density or fluid element. In the straightforward way, our formula can be
applied in other fields of physics, wherever one deals with hot and
relativistic matter.
