Evidence for non-ergodicity in quiescent states of periodically sheared suspensions

TL;DR

This study compares equilibrium and non-equilibrium models of quiescent states in periodically sheared suspensions, revealing non-ergodicity and differences in structural properties, phase transitions, and hyperuniformity.

Contribution

It demonstrates that dynamical protocols do not uniformly sample all quiescent states, highlighting non-ergodicity and differences in structural and phase transition behaviors.

Findings

Non-equilibrium model states differ structurally from equilibrium states.

Hyperuniform states are accessible via non-equilibrium protocols but not through ergodic sampling.

Phase and percolation transitions are present in equilibrium but absent in non-equilibrium models.

Abstract

We present simulations of an equilibrium statistical-mechanics model that uniformly samples the space of quiescent states of a periodically sheared suspension. In our simulations, we compute the structural properties of this model as a function of density. We compare the results of our simulations with the structural data obtained in the corresponding non-equilibrium model of Cort\'e et al. [Nat. Phys. 4, 420 (2008)]. We find that the structural properties of the non-equilibrium model are very different from those of the equilibrium model, even though the two models have exactly the same set of accessible states. This observation shows that the dynamical protocol does not sample all quiescent states with equal probability. In particular, we find that, whilst quiescent states prepared in a non-equilibrium protocol can be hyperuniform [see Phys. Rev. Lett. 114, 110602 (2015), Phys. Rev. Lett. 114, 148301 (2015), and Phys. Rev. Lett. 115, 108301 (2015)], ergodic sampling never leads to hyperuniformity. In addition, we observe ordering phase transitions and a percolation transition in the equilibrium model that do not show up in the non-equilibrium model. Conversely, the quiescent-to-diffusive transition in the dynamical model does not correspond to a phase transition, nor a percolation transition, in the equilibrium model.