  Understanding granular and other athermal systems requires the identification
of state variables which consistently predict their bulk properties. A
promising approach has been to draw on the techniques of equilibrium
statistical mechanics, but to consider alternate conserved quantities in place
of energy. The Edwards ensemble, based on volume conservation, provides a
temperaturelike intensive parameter called compactivity. We present experiments
which demonstrate the failure of compactivity to equilibrate (via
volume-exchange) between a pair of externally-agitated granular subsystems with
different material properties. Nonetheless, we identify a material-independent
relationship between the mean and fluctuations of the local packing fraction
which forms the basis for an equation of state. This relationship defines an
intensive parameter that decouples from the volume statistics.
