  Although generalized ensembles have now been in use in statistical mechanics
for decades, including frameworks such as Tsallis' nonextensive statistics and
superstatistics, a classification of these generalized ensembles outlining the
boundaries of validity of different families of models, is still lacking. In
this work, such a classification is proposed in terms of supercanonical and
subcanonical ensembles, according to a newly defined parameter, the inverse
temperature covariance parameter $\mathcal{U}$. This parameter is non-negative
in superstatistics (and is equal to the variance of the inverse temperature)
but can be negative for other families of statistical ensembles, adquiring then
a broader meaning. It is shown that $\mathcal{U}$ is equal for every region of
a composite system in a steady state, and examples are given of supercanonical
and subcanonical states.
