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 f(x,y); one can write

Let , and , thus

If one subtracts d(qy) from df, one has

or

Defining the function g = f − qy then

The partial derivatives of g are

.

[edit] Example

[edit] See also

• Thermodynamic relations

[edit] References

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