On `The conformal metric structure of Geometrothermodynamics': Generalizations

We show that the range of applicability of the change of representation formula derived in J. Math. Phys. $\mathbf{\text{54}}$, 033513 (2013) [arXiv:1302.6928] is very narrow and extend it to include all physical applications, particularly, applications to black hole thermodynamics, cosmology and fluid thermodynamics.