  The dynamics of one and two identical spheres rolling in a nearly-levitating
upflow of air obey the Langevin Equation and the Fluctuation-Dissipation
Relation [Ojha et al. Nature 427, 521 (2004) and Phys. Rev. E 71, 01631
(2005)]. To probe the range of validity of this statistical mechanical
description, we perturb the original experiments in four ways. First, we break
the circular symmetry of the confining potential by using a stadium-shaped
trap, and find that the velocity distributions remain circularly symmetric.
Second, we fluidize multiple spheres of different density, and find that all
have the same effective temperature. Third, we fluidize two spheres of
different size, and find that the thermal analogy progressively fails according
to the size ratio. Fourth, we fluidize individual grains of aspherical shape,
and find that the applicability of statistical mechanics depends on whether or
not the grain chatters along its length, in the direction of airflow.
