Geometrothermodynamics: comments, criticisms, and support

We write explicitly the Euler identity and the Gibbs–Duhem relation for thermodynamic potentials that are not homogeneous first-order functions of their natural extensive variables. We apply the rules to the theory of geometrothermodynamics and show how the use of the natural extensive variables, instead of the modified ones, leads to misleading results. We further reveal some other ambiguities and inconsistencies in the theory and we make new suggestions.