Metric geometry of equilibrium thermodynamics. II. Scaling, homogeneity, and generalized Gibbs–Duhem relations

It is shown that the classical Gibbs–Duhem relation can be regarded, in the abstract metric framework proposed recently, as expressing the obvious geometric impossibility of finding r + 1 linearly independent vectors in an r-dimensional space. Certain connections between generalized Gibbs–Duhem relations and permissible scaling hypotheses for thermodynamic potentials are noted.