Random very loose packs
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 = phircp, and a low density, at phi = phirvlp, where phirvlp is a new lower bound we call random very loose pack. phirlp 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 < phirlp are characterized by a negative temperature.
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