Temperature-dependent energy levels and size-independent thermodynamics.

We show that, by properly adopting the notion of temperature-dependent energy levels, the standard tools of differential thermodynamics can be used for a consistent thermostatistical description irrespective of system size. In this framework the paradigmatic (yet not always descriptive) large-system limit is no longer a necessary assumption for differential thermodynamics. We present a generalized relation between temperature and internal energy which extends thermodynamics all the way to isolated quantum systems.