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I don't remember where I read it, or even if my memory serves me correctly, but I think that I read somewhere that the Lie derivative amounts to a Legendre transform. Is this true and, if it is, what is the relation between them?

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    $\begingroup$ I would be amazed if there were one! Do you have any idea what context you heard this in? $\endgroup$ – knzhou May 28 at 0:16
  • $\begingroup$ I vaguely remember in thermodynamics, if you take Lie derivative of a differential form on a 2*n+1 manifold, you get back the differential form times a partial derivative - which was the Legendre transform. We didn't use it much. $\endgroup$ – Cinaed Simson May 28 at 7:22
  • $\begingroup$ Here's the URL for the "Geometry of Thermodynamic Processes" - arxiv.org/abs/1811.04227. The paper uses the Lie derivative to compute Legendre transformations. $\endgroup$ – Cinaed Simson May 28 at 22:10
  • $\begingroup$ Thanks Cinaed. I downloaded the paper and will read it when I get home. $\endgroup$ – OHC May 30 at 4:27

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