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
References
- Mary L. Boas "Mathematical methods in the Physical Sciences" John Wiley & Sons, Second Edition.