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RE: HELP: Legendre transform

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  • Subject: [mg5633] RE: [mg5619] HELP: Legendre transform
  • From: "Artz, Ray E @EAG" <ray.e.artz at>
  • Date: Wed, 1 Jan 1997 21:04:59 -0500
  • Encoding: 30 TEXT
  • Sender: owner-wri-mathgroup at

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
artz0002 at

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