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

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Abstract
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.