Entropy and Order Parameters in Granular Media Under Shear

Povzetek

Dense granular media under shear can jam or flow depending on packing fraction and shear history, but the
relationship between microstructural order and configurational (packing) entropy across this transition is not fully
quantified. We used discrete element method (DEM) simulations of bidisperse frictional disks under quasi-static
simple shear to jointly track a scalar order parameter, based on local hexagonal bond-orientational order, and
configurational entropy, estimated from the Voronoi cell-shape distribution, across 60 independent realizations
spanning packing fractions from 0.76 to 0.87. Configurational entropy per particle fell monotonically from 1.42 ±
0.06 k_B at the loosest packing fraction tested (0.76) to 0.51 ± 0.05 k_B near jamming (0.87), while the hexagonal
order parameter rose from 0.18 ± 0.03 to 0.61 ± 0.04 over the same range, and the two quantities were strongly
anti-correlated across all realizations (Pearson r = -0.93, p < 0.001, n = 60). A sharp inflection in both quantities
occurred at a packing fraction of 0.843 ± 0.004, closely bracketing the independently measured shear-jamming
point at 0.841 ± 0.003 identified from the onset of sustained pressure under applied shear strain, with 71% of the
total entropy drop across the full packing-fraction range occurring within a narrow window of ±0.02 around this
inflection. Force-chain anisotropy, quantified from the fabric tensor, increased sharply in the same narrow window,
rising from 0.09 to 0.34, and its onset coincided with the entropy inflection to within the packing-fraction resolution of
the study (0.002). A finite-size check using system sizes from 2,000 to 8,000 particles showed the inflection packing
fraction shifted by less than 0.003 and the peak entropy-drop rate changed by less than 6%, indicating the transition
signature is not a finite-size artifact over this range. These results establish configurational entropy collapse as a
quantitative, structurally grounded signature of the shear-jamming transition that tracks closely with, and largely
precedes, the onset of measurable force-chain anisotropy, offering a packing-based diagnostic for jamming onset
that does not require direct stress measurement.