Generalized Phase Rule and Possible Singular Point Sets in Physical Systems

Abstract

There have been phase rules of coexistence point sets (Gibbs phase rule) and of critical point sets (Griffiths phase rule) in one order parameter systems. Other than these singular point sets, we have complex singular point sets like the critical end point and the critical double point which are attracting attentions recently. The generalized phase rule has been proved for all of these singluar point sets in a system with an arbitrary number of order parameters. It includes the Gibbs phase rule and the Griffiths phase rule as special cases. All possible singular point sets and their variance in relatively simple physical systems are also tabulated from the point of view of the catastrophe theory.