Metric geometry of equilibrium thermodynamics. V. Aspects of heterogeneous equilibrium

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Abstract
The general analysis of phase equilibrium in heterogeneous systems is considered from an abstract geometric point of view. Particular attention is drawn to the thermodynamic ’’invariants’’ (or ’’symmetries’’), which arise as null eigenvectors of the thermodynamic metric matrix and can be associated with variations which leave the thermodynamic state unchanged. The analysis of these invariants leads to conditions connecting the thermodynamic field vectors, including Gibbs–Duhem relations, Clausius–Clapeyron equations, Gibbs–Konowalow laws, and systematic generalizations thereof.