On the classification of singularities in thermodynamics

The occurrence of Legendrian singularities in thermodynamics is discussed. In fact, the stability condition strongly limits the list of such singularities having a physical relevance (related to critical phenomena). Another type of singularities, due to the convexification of the internal energy, does intervene. Such singularities are related to phase transitions. The complete list of generic phenomena occurring in binary mixtures is obtained through the classification of these singularities.