Legendre transform

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The Legendre transform (Adrien-Marie Legendre) is used to perform a change change of variables (see, for example, Ref. 1, Chapter 4 section 11 Eq. 11.20 - 11.25):

If one has the function one can write

Let , and , thus

If one subtracts from , one has

or

Defining the function then

The partial derivatives of are

.

Example

See also

References

  1. Mary L. Boas "Mathematical methods in the Physical Sciences" John Wiley & Sons, Second Edition.
  2. R. A. Alberty "Use of Legendre transforms in chemical thermodynamics", Pure and Applied Chemistry 73 pp. 1349-1380 (2001)