When two isolated system are brought in contact, they relax to equilibrium via energy exchange. In another setting, when one of the systems is driven and the other is large, the first system reaches a non-equilibrium steady-state. We show that the size of energy fluctuations as a function of time is universal in both settings, assuming that the process is composed of many small steps of energy exchange. The results depend only on the average energy flows in the system and the density of states, independent of any other microscopic detail. In the steady-state we also derive an expression relating three key properties: the relaxation time of the system, the energy injection rate, and the size of the fluctuations.
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