Legendre transform theory is: (1) developed to show the relationships among the common thermodynamic potential functions (that is, energy, enthalpy, and free energy); (2) extended to introduce other potential functions which are particularly convenient in certain applications (for example, stability and critical point phenomena of multicomponent systems). General derivative operators are employed to allow partial derivatives of a given potential functions to be transformed to derivatives of other potential functions.
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Beegle et al. (1974) studied this question.
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