Generalized Massieu-Planck functions: Geometric representation, extrema and uniqueness properties

Massieu-Planck functions are thermodynamic transforms closely related to the more familiar Legendre transforms. They arise naturally in the theory of concentration and entropy fluctuations in multicomponent systems. Generalization of the Massieu-Planck transform concept gives rise to a one-to-one correspondence between each thermodynamic potential and an associated Massieu-Planck function having the same uniqueness and extrema properties. The specific Massieu-Planck functions arising in fluctuation theory are particular cases of the transforms whose algebraic and geometric properties are presented here.