  A general formulation of stochastic thermodynamics is presented for open
systems exchanging energy and particles with multiple reservoirs. By
introducing a partition in terms of "macrostates" (e.g. sets of "microstates"),
the consequence on the thermodynamic description of the system is studied in
detail. When microstates within macrostates rapidly thermalize, the entire
structure of the microscopic theory is recovered at the macrostate level. This
is not the case when these microstates remain out of equilibrium leading to
additional contributions to the entropy balance. Some of our results are
illustrated for a model of two coupled quantum dots.
