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Phys Rev Lett. 2008 Sep 19;101(12):128001. Epub 2008 Sep 15.

Random very loose packings.

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CNISM and Department of Information Engineering, Second University of Naples, 81031 Aversa (CE), Italy.


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)=logOmega(phi) vanishes both at high density, at phi approximately equal to phi_rcp, and a low density, at phi approximately equal to 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.

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