Existence of non-equilibrium indifferent states

It can be shown that if we do not confine ourselves to equilibrium states, the necessary condition that a given closed system can exist in an indifferent state is that  

For of the relations A, B and C enumerated in the previous paragraph, the equations B only are conditions of equilibrium. If we do not limit ourselves to equilibrium states, then these equations need not be satisfied. On the other hand equations A and C must be satisfied by all systems in an indifferent state, whether or not in equilibrium. 

As we have seen in the previous paragraph, if the conditions of enclosure (29.108) are to have a solution in. ... .. / when 

Let us suppose that we are given the initial masses at random, and let us enquire whether the closed system thus constituted can exist in an indifferent state, whether static or not. This clearly cannot be possible unless there exists an indifferent state in which the weight fractions satisfy the 1-f-c - (0-f-/) conditions of compatibility. However, the composition variables must also satisfy the 1- (r + r ) equations A. In all we have therefore 

We note that algebraically this condition is generally both necessary and sufficient. If, however, the algebraic solution gives negative values for one or more of the then the solution is not physically significant. Thus the condition (29.124) is always a necessary condition, but is not always sufficient. 

---