Change of variables in thermodynamics

The problem of which transformations of variables leave thermodynamics laws invariant is considered. It is shown that contact transformations in the space of odd dimensionality spanned by all the fields and density variables together provide the solution of the classical problem. It is also shown that in this framework it is possible to give a consistent ''derivation'' of the Gibbs phase rule which Avoids the introduction of the ''metastable'' extension of the one-phase equilibirum surfaces