Probing ergodicity in granular matter

TL;DR

This study investigates whether granular systems under tapping exhibit ergodic behavior by comparing ensemble and time-based volume histograms, ultimately finding nonergodicity and inconsistency with Edwards' hypothesis.

Contribution

The paper introduces a new method to evaluate ergodicity in granular matter and demonstrates nonergodic behavior through histogram comparisons.

Findings

Granular systems show nonergodic volume behavior.

Histograms are incompatible with Edwards' canonical assumption.

New assessment method for ergodicity in granular systems.

Abstract

When a granular system is tapped, its volume changes. Here, using a well-defined macroscopic protocol, we prepare an ensemble of granular systems and track the statistics of volume changes as a function of the number of taps. This is in contrast to previous studies, which have focused on single trajectories and assumed ergodicity. We devise a new method to assess the convergence properties of a sequence of ensemble volume histograms and introduce a reasonable approximate version of an invariant histogram. We then compare these invariant histograms with histograms generated by sampling a long trajectory for one system and observe nonergodicity, which we quantify. Finally, we use the overlapping histogram method to assess potential compatibility with Edwards' canonical assumption. Our histograms are incompatible with this assumption.