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What Is Entropy?

(jasonfantl.com)
287 points jfantl | 4 comments | 14 Apr 25 18:32 UTC | HN request time: 0.001s | source
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karpathy ◴[14 Apr 25 21:43 UTC] No.43686645[source]▶
What I never fully understood is that there is some implicit assumption about the dynamics of the system. So what that there are more microstates of some macrostate as far as counting is concerned? We also have to make assumptions about the dynamics, and in particular about some property that encourages mixing.
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tomnicholas1 ◴[14 Apr 25 21:56 UTC] No.43686753[source]▶
Yes, that assumption is called the Ergodic Hypothesis, and generally justified in undergraduate statistical mechanics courses by proving and appealing to Liouville's theorem.

[1] https://en.wikipedia.org/wiki/Ergodic_hypothesis

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1. vitus ◴[14 Apr 25 22:32 UTC] No.43687018[source]▶
It's worth noting that there's more than just ergodicity at play, although that's a fundamental requirement. For instance, applying the Pauli Exclusion Principle gives rise to Fermi-Dirac statistics.
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2. tomnicholas1 ◴[14 Apr 25 22:41 UTC] No.43687087[source]▶
Isn't that more about enumerating the microstates? The Pauli exclusion principle just ends up forbidding some of the microstates (forbidding a significant fraction of them if you're in the low-temperature regime).
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3. vitus ◴[14 Apr 25 22:45 UTC] No.43687112[source]▶
It is about enumerating the microstates, but in a way that takes into account how the particles interact with each other (aka making assumptions about the dynamics).

If we didn't take into account any interactions, we'd be unable to do anything with statistical mechanics beyond rederiving the ideal gas law.

replies(1): >>43687749 #
4. ◴[15 Apr 25 00:22 UTC] No.43687749{3}[source]▶