  We combine the shear-transformation-zone (STZ) theory of amorphous plasticity
with Edwards' statistical theory of granular materials to describe shear flow
in a disordered system of thermalized hard spheres. The equations of motion for
this system are developed within a statistical thermodynamic framework
analogous to that which has been used in the analysis of molecular glasses. For
hard spheres, the system volume $V$ replaces the internal energy $U$ as a
function of entropy $S$ in conventional statistical mechanics. In place of the
effective temperature, the compactivity $X = \partial V / \partial S$
characterizes the internal state of disorder. We derive the STZ equations of
motion for a granular material accordingly, and predict the strain rate as a
function of the ratio of the shear stress to the pressure for different values
of a dimensionless, temperature-like variable near a jamming transition. We use
a simplified version of our theory to interpret numerical simulations by
Haxton, Schmiedeberg and Liu, and in this way are able to obtain useful
insights about internal rate factors and relations between jamming and glass
transitions.
