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May 14, 2023 at 21:00 comment added Tom Copeland For more on Willerton;s approach, see golem.ph.utexas.edu/category/2023/05/….
May 14, 2023 at 4:03 comment added Tom Copeland I really should mention Fermat's, Maupertuis', and Hamilton and Jacobi's principles as well to indicate the traditional use of the term 'principle' in geometric optics and particle propagation. .
May 14, 2023 at 2:59 comment added Tom Copeland Lawvere mentions the Bellman-Fenchel convolution in "Metric spaces, generalized logic, and closed categories", not directly the Legendre-Fenchel transform, but Bellman and Karush in "The maximum transform" reference Fenchel's "Convex cones, sets, and functions", so I assume they are basically talking about the same constructions, as Willerton indicates.
May 14, 2023 at 0:10 comment added Tom Copeland In thermodynamics, there is a similar connection between the Legendre-Fenchel transform and the minimization of energy and the maximization of entropy, which I believe is currently a popular topic among categorists.
May 14, 2023 at 0:06 history answered Tom Copeland CC BY-SA 4.0