Equivalence of fluctuation-dissipation and Edwards' temperature in cyclically sheared granular systems

TL;DR

This study demonstrates that in cyclically sheared granular systems, the effective temperature derived from fluctuation-dissipation relations matches the Edwards' compactivity, indicating a thermodynamic-like behavior.

Contribution

The paper provides empirical evidence that fluctuation-dissipation and Edwards' temperatures are equivalent in sheared granular materials, bridging dynamical and configurational descriptions.

Findings

Excellent agreement between the two temperatures across conditions

Temperature equivalence is independent of tracer type and shear amplitude

Broken contact symmetry causes viscous-like drag force in granular systems

Abstract

Using particle trajectory data obtained from x-ray tomography, we determine two kinds of effective temperatures in a cyclically sheared granular system. The first one is obtained from the fluctuation-dissipation theorem which relates the diffusion and mobility of lighter tracer particles immersed in the system. The second is the Edwards compactivity defined via the packing volume fluctuations. We find robust excellent agreement between these two temperatures, independent of the type of the tracers, cyclic shear amplitudes, and particle surface roughness. We further elucidate that in granular systems the viscous-like drag force is due to the broken symmetry of the local contact geometry.