Random very loose packs

TL;DR

This paper investigates the number of mechanically stable granular states across different volume fractions, introducing a new lower bound called the random very loose pack, and explains experimental compaction results.

Contribution

It defines the random very loose pack volume fraction and provides a first-principles explanation for granular packing behavior.

Findings

Entropy vanishes at high and low densities

Identifies a new lower bound phi_rvlp for loose packing

States with phi < phi_rlp have negative temperature

Abstract

We measure the number Omega(phi) of mechanically stable states of volume fraction phi of a granular assembly under gravity. The granular entropy S(phi) = log Omega(phi) vanishes both at high density, at phi = phi_rcp, and a low density, at phi = phi_rvlp, where phi_rvlp is a new lower bound we call random very loose pack. phi_rlp is the volume fraction where the entropy is maximal. These findings allow for a clear explanation of compaction experiments, and provide the first first-principle definition of the random loose volume fraction. In the context of the statistical mechanics approach to static granular materials, states with phi < phi_rlp are characterized by a negative temperature.