  We compare the predictions of two different statistical mechanics approaches,
corresponding to different physical measurements, proposed to describe binary
granular mixtures subjected to some external driving (continuous shaking or tap
dynamics). In particular we analytically solve at a mean field level the
partition function of a simple hard sphere lattice model under gravity and we
focus on the phenomenon of size segregation. We find that the two approaches
lead to similar results and seem to coincide in the limit of very low shaking
amplitude. However they give different predictions of the crossovers from
Brazil nut effect to reverse Brazil nut effect with respect to the shaking
amplitude, which could be detected experimentally.
