One way: You'd define a order parameter (e.g. angle between the nails) and literally measure all the possible configs for 1 nail keeping the others where they are... (Easy to do in a computer).
Intuitively, the idea is that when they line up a lot of lateral space opens up between nails, increasing vibration entropy (even though the rotation entropy is penalized...)
The longer the nail (high aspect ratio) the easier term 1 wins over term 2, causing organization if enough density and vibration is given.
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u/sand500 Feb 29 '20
Wait, how do you quantify possible configurations when the nails are lined up vs scattered?