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In the coexistence region, g ( r ) has more peaks than those of random packings, but the magnitude of the peaks decays very fast as the distance r becomes larger. The long-range order increases with the volume fraction in the coexistence region. 

## IV. THERMODYNAMIC VIEWPOINT OF THE RCP TRANSITION 

## A. Free energy 

In the thermodynamics of jammed matter, the internal energy U is replaced by the volume W (usually called the volume function) [21]. Other thermodynamic potentials, such as enthalpy H , free energy F , Gibbs free energy G , are related to the volume function W as 

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