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Recent advances in quantum thermodynamics have been focusing on ever moreelementary systems of interest, approaching the limit of a single qubit, withcorrelations, strong coupling and non-equilibrium environments coming intoplay. Under such scenarios, it is clear that fundamental physical quantitiesmust be revisited. This article questions whether a universal definition ofinternal energy for open quantum systems may be devised, setting limits on itspossible properties. We argue that, for such a definition to be regarded aslocal, it should be implemented as a functional of the open system's reduceddensity operator and its time derivatives. Then we show that it should involveat least up to the second-order derivative, otherwise failing to recover thepreviously-known internal energy of the "universe". Possible implications ofthis general result are discussed.

A constraint on local definitions of quantum internal energy