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I recently asked a question on the Physics stack exchange: Derivation of temperature / entropy relation from statistical mechanics. It was put on hold for being 'off-topic'.

The question looks like a banal homework question but I think it is actually a good example of the barrier between immediately linking statistical mechanics and thermodynamics. I start with some very standard statistical mechanics definitions and try to derive a well known equality from thermodynamics. The derivation fails and I don't think this is through mathematical error. I have written what I think is the answer, but a commenter has suggested that it goes deeper than that. In any case, the answer is not obvious to me and commenters on the question have agreed.

Can it be re-opened?

P.S. I hope I'm following etiquette by posting in here, I'm following these guidelines.

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A good example of a question which is more subtle than it appears on a casual read, and an appropriate use of Meta as part of the re-opening process. We're glad to have you here as a contributor.

Now that your question is re-opened, consider posting your answer (preserved in the question's revision history) as a proper answer.

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