Edwards thermodynamic framework controls density segregation in cyclically sheared granular materials

Granular segregation is a widespread phenomenon observed in various industrial applications, geophysical processes, and daily life events. It can be driven by multiple mechanisms, and numerous models have been proposed to elucidate this behavior. However, most of these models are phenomenological and qualitative, lacking a unified theoretical framework based on statistical mechanics. Using x-ray tomography, we experimentally investigate granular segregation phenomena in a mixture of particles with different densities under quasistatic cyclic shear. Our findings demonstrate that in regions where particles have sufficient accumulated strain for structural relaxation, their steady-state height distributions can be quantitatively characterized by minimizing an effective free energy based on a segregation temperature that captures the competition between the mixing entropy and gravitational potential energy. We find this temperature coincides with Edwards' compactivity within error under various pressures and cyclic shear amplitudes. Therefore, we find that granular segregation in quasistatic conditions can be fundamentally explained by an effective granular thermodynamic framework including real energy terms based on the Edwards statistical ensemble.