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FIG. 12: The distribution of entropy S (ln p, ln( φ − φ$_{c}$ )) along the direction ( − sin θ, cos θ ) for different jamming ensemble points. The blue ○ are the entropy for jammed system, which is the maximum of S , verifying the second law of thermodynamics. We notice that some deviations are found near φ$_{c}$ . 

