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Owen Lynch (Jan 28 2022 at 15:14):This is from https://arxiv.org/pdf/1811.04227.pdf
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Owen Lynch (Jan 28 2022 at 15:14):This analogy should be made precise with a coarse-graining argument
John Baez (Jan 29 2022 at 19:00):Sounds good! There are a couple of small "flaws" in our paper (which we should really submit for publication soon):
We don't ever prove any theorems that absolutely require convexity/concavity, though it's present in all our examples and it's obviously important.
We don't explain how the convex structure in the stat mech examples - taking mixtures of mixed states - is related to the convex structure in the thermo examples.
John Baez (Jan 29 2022 at 19:15):I don't know if we should fix these, but maybe we should point them out as issues for future work.