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then your OP is less mysterious, because the disorder of the total system has increased, it's just not localized in flakes to which we attend.
No, you're still missing the point. The *apparent* disorder has decreased. The freezer with ice crystals in it looks more organized than when it had liquid water. That's the entire point: apparent disorder as perceived by humans is not the same as thermodynamic entropy.
i don't think we need to go so far as to say who has missed a point when we've both nudged points of clarity.
I still think your OP, as stated, is just false: "The snowflake has higher entropy (2nd law) than the water + air system that formed it" ... No
I agree we humans do suck at seeing air molecules move around.
There are some systems where a crystalline state actually has higher entropy than the corresponding liquid state! For instance, consider a packing of chopsticks or other hard rods (a crude model for the nematic liquid crystals in LCDs). Compare the "crystalline" state where ...
the rods are aligned to the "liquid" state where the rods are pointing in random directions. At sufficiently high fixed density, the *aligned* rods are entropically preferred because they have much more space to move around than the randomly-oriented rods.
But isn't the whole point that the perception is flawed because we *can't* see the rest of the closed system, e.g. we are not imaging the substrate in thermal IR to see it warm up, imaging the surrounding air so we can see the swirls of air currents, etc?
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