My brain can’t understand this at all. In an isolated system with cold molecules on one side and hot molecules on the other, I understand how the heat of this system balances with time, but it’s confusing to me that a system with a more evenly distributed temperature has increased randomness when it appears that there’s more order.
This feels like it should be simple, but my brain simply isn’t getting it, no matter how many analogies or examples I read. I’ve got to be missing something very simple, and that’s why it’s so frustrating that I don’t understand it. This is seriously stressing me out.
In: Physics
So, entropy has a mathematical definition (well, several, but this one applies here). Entropy is not just “disorder,” it’s “the number of ways a system can be arranged.”
Entropy= k*ln(W), where k is a constant and W is the number of ways a system can be arranged.
So imagine a box which perfectly fits 10 balls. They are all identical white balls, so no matter what you do, there is only 1 way to arrange them. Log of 1 is 0 so there is literally zero entropy.
If you swap 1 white ball for a black ball, now the black ball could be in 10 different “otherwise identical states.” So there would be 10 ways to arrange this system.
If you had 5 white balls on one side, and 5 black balls on the other side, again there would only be one way to arrange this. If you allow 1 ball if each color to cross over to the other side, the number of ways to arrange it increases.
So statistically, if you put a bunch of balls in a box and shook them up, it’s some million times more likely that they would be mixed up, rather than evenly divided on each side. But there’s not some “force” pushing it this way.
You can imagine the balls like atoms, and heat is like shaking it up. They will settle in a “more likely” configuration, which is how we define maximum entropy.
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