Detailed balance in non-equilibrium dynamics of granular matter: derivation and implications

Abstract

Modelling the dynamics of dense granular media is a long standing challenge and essential to many natural phenomena and technological applications. Here, we trace back puzzling experimental observation of detailed-balanced steady states to self-organisation of the neighbour probability distribution. The emergence of detailed balance in non-equilibrium granular dynamics could constitute a major step toward better models of granular media, as well as provide more insight into non-equilibrium processes in general. We show analytically that DBSS emerges when a certain neighbour probability is uniform across the system. This condition leads to a conditional cell order distribution being independent of the condition. We then carry out rotational shear experiments, in which this condition is satisfied, and show that they give rise to robust detailed-balanced steady states. We also show that, when the unconditional cell order distribution maximises the entropy, it is determined by a single constant parameter that is characteristic of all cell transitions. These results illustrate the predictive power of recently proposed evolution equations, which pave the way to simpler models of the dynamics of planar granular systems.