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We derive a formula that defines quantum fluctuations of energy in subsystemsof a hot relativistic gas. For small subsystem sizes we find substantialincrease of fluctuations compared to those known from standard thermodynamicconsiderations. However, if the size of the subsystem is sufficiently large, wereproduce the result for energy fluctuations in the canonical ensemble. Ourresults are subsequently used in the context of relativistic heavy-ioncollisions to introduce limitations of the concepts such as classical energydensity or fluid element. In the straightforward way, our formula can beapplied in other fields of physics, wherever one deals with hot andrelativistic matter.

Quantum fluctuations of energy in subsystems of a hot relativistic gas