  Recent advances in quantum thermodynamics have been focusing on ever more
elementary systems of interest, approaching the limit of a single qubit, with
correlations, strong coupling and non-equilibrium environments coming into
play. Under such scenarios, it is clear that fundamental physical quantities
must be revisited. This article questions whether a universal definition of
internal energy for open quantum systems may be devised, setting limits on its
possible properties. We argue that, for such a definition to be regarded as
local, it should be implemented as a functional of the open system's reduced
density operator and its time derivatives. Then we show that it should involve
at least up to the second-order derivative, otherwise failing to recover the
previously-known internal energy of the "universe". Possible implications of
this general result are discussed.
