Comment by raattgift

Crystals are very uniform and yet have very low entropy: at 0 K the entropy of a perfect crystal is zero. See <https://en.wikipedia.org/wiki/Third_law_of_thermodynamics#Ex...>.

Your second paragraph is not a million miles off from Boltzmannian entropy, the log relationship between a macrostate and the set of microstates that match the macrostate. A very carefully layered milk-on-coffee matches no microstates in which there is milk at the bottom of the arrangement or coffee at the top. A fully stirred mix can have a milk molecule and a coffee molecule anywhere in the mix: this matches a much larger set of microstates than the layered case.

It's mostly molecular translation and rotation (hurried up by the stirring) that causes the layered milk-on-coffee to homogenize and come into thermal equilibrium.

But if we take the perfect crystal case, any microscopic rotation or translation within the crystal makes the crystal LESS uniform but also dramatically increases the crystal's entropy.

If we smash the crystal into dust the entropy will become much higher, but the dust will be arranged much less uniformly than when the crystal was intact.

> entropy is a measure of order

Yes.

> or how mixed things are

Maybe.

> Entropy can also be understood as uniformity

Sometimes. There are lots of things in nature which are highly uniform but have very low entropy, with entropy increasing as they become less uniform.