Quick entropy lesson: the way entropy is thermodynamically defined (one of the ways) is that entropy S = kB ln Omega, where kB is Boltzmann's constant, ln is the natural logarithm (an increasing function) and Omega is the number of possible microstates with a given macrostate. Which means that the higher the entropy, the more possible orientations. It's right in the definition that more entropy means more "possibilities," even as there's less order.
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Fascinating. Thank you.