Gibbs' phase rule was proposed by Josiah Willard Gibbs in his landmark paper titled On the Equilibrium of Heterogeneous Substances, published from 1875 to 1878. The rule applies to non-reactive multi-component heterogeneous systems in thermodynamic equilibrium and is given by the equality

where F (alternatively G) is the number of degrees of freedom, C (alternatively N) is the number of components and P (alternatively p or F) is the number of phases in thermodynamic equilibrium with each other.