Generalization of the Gibbs-Konovalow theorems

We met these theorems in studying the properties of states of uniform composition (chap. XVIII, 6) we shall now examine them in a more general form as a property of all static indifferent states in a poly variant system. 

These theorems, in which we consider the effect either of an isothermal or isobaric displacement were demonstrated by Gibbs and Konovalow for bivariant systems and generalized by Saurel. They can only be applied to systems having a variance of at least two systems of smaller variance are not susceptible to such displacements. 

If in any isothermal equilibrium displacement the system passes through an indifferent state, then the pressure passes through an extreme value. 

among the pressures which maintain the system in equilibrium at a constant temperature, there exists an extreme value of then the state corresponding to this extreme value is an indifferent state. 

In dealing with polyvariant systems it must be remembered that the pressure cannot be regarded as exhibiting an extreme value at a given point unless it represents an extreme  

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