alright just for fun: AMA but only about math, will attempt to speed-explain stuff with as few symbols and equations as possible and see what happens
(esp happy to field questions about stuff that seems basic to you and that you feel like you should've gotten a long time ago!)
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legendre transform keeps coming up (& now again in those thermodynamics notes) and I keep looking at definitions and getting zero intuition but people keep talking like there is some pretty good intuition possible?
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i unfortunately do not really get it either but i agree that there is something to get. the version of it i get the most is the one that appears in large deviations which appears through a more or less straightforward calculation: