  Granular matter exists out of thermal equilibrium, i.e. it is athermal. While
conventional equilibrium statistical mechanics is not useful for characterizing
granular materials, the idea of constructing a statistical ensemble analogous
to its equilibrium counterpart to describe static granular matter was proposed
by Edwards and Oakshott more than two decades ago. Recent years have seen
several implementations of this idea. One of these is the stress ensemble,
which is based on properties of the force moment tensor, and applies to
frictional and frictionless grains. We demonstrate the full utility of this
statistical framework in shear jammed (SJ) experimental states [1,2], a special
class of granular solids created by pure shear, which is a strictly
non-equilbrium protocol for creating solids. We demonstrate that the stress
ensemble provides an excellent quantitative description of fluctuations in
experimental SJ states. We show that the stress fluctuations are controlled by
a single tensorial quantity: the angoricity of the system, which is a direct
analog of the thermodynamic temperature. SJ states exhibit significant
correlations in local stresses and are thus inherently different from
density-driven, isotropically jammed (IJ) states.
