RE: HELP: Legendre transform
- To: mathgroup at smc.vnet.net
- Subject: [mg5633] RE: [mg5619] HELP: Legendre transform
- From: "Artz, Ray E @EAG" <ray.e.artz at lmco.com>
- Date: Wed, 1 Jan 1997 21:04:59 -0500
- Encoding: 30 TEXT
- Sender: owner-wri-mathgroup at wolfram.com
GB wrote: ...I understand the steps involved in taking the Legendre transform (often found in thermodynamics derivations, and not to be confused with the Laplace transform), but I have no intuitive feeling for what's going on... _____________________ I can't help with a Mathematica program, but I can suggest that the "best" way to view the Legendre transform (at least in many applications) is from the viewpoint of convex analysis. Since you mentioned thermodynamics, a good place to start would be Wightman's introduction (actually an expository essay on the history of convexity methods in thermodynamics) to Israels monograph "Convexity in the Theory of Lattice Gasses". The standard reference on Convex Analysis is the text "Convex Analysis" by Rockafellar, but I am not too familiar with it. I personally found the first chapter of "Convex Analysis and Minimization Algorithms" by Hiriart-Urruty and Lemarechal very readable and insightful. GB: This is a topic that I am currently interested in, especially for statistical applications. Please report your progress to Mathgroup and/or me personally. (Also feel free to contact me you can't find the references (I may have misspelled, etc.) Ray Artz ray.e.artz at lmco.com artz0002 at gold.tc.umn.edu