Does an Edwards-type ensemble describe granular packings away from jamming
In plain words
Edwards proposed that all stable arrangements of grains at a given volume are equally likely, which would give packed grains a statistical mechanics like that of a gas. Computer counting found this true only exactly at the jamming point, and whether some modified ensemble works for real, frictional, tapped or sheared grains is unknown.
Precise statement
The Edwards hypothesis assigns equal probability to all mechanically stable packings at fixed volume V, with entropy $S(V) = \ln \Omega(V)$ and compactivity $X = dV/dS$. Direct enumeration for frictionless soft disks found the flat measure holds only at the jamming density $\phi_J$. For frictional grains in steady states produced by tapping or cyclic shear, determine whether packing statistics depend only on intensive variables (compactivity, angoricity) and not on the protocol, and give the correct ensemble if the flat measure fails.
What would settle it
Experiments or simulations in which different protocols reach the same volume and stress, testing whether the distributions of local volumes and contact forces coincide, together with an ensemble that predicts them.
Status in the literature
Unverified note
In 2017 numerical enumeration showed that all packings are equally probable at jamming but not above it (Martiniani et al., Nature Physics, https://doi.org/10.1038/nphys4168); the frictional, driven case is open (2026).