Stability with respect to diffusion in a c-component system

Stability with respect to Diffusion in a c-Component System. 

We return to the problem of stability with respect to diffusion studied in 12, but now we consider the case of a system containing any number of components. To achieve the greatest symmetry we introduce as many reaction variables. .. c there are components. Each extent of change corresponds to passage of component i from the volume element a to 6. 

On the other hand the chemical potentials and may be expressed as functions of T, p and the numbers of moles of the various components. Because of (15.75) we see that /x T, jp, nf, n ) depends on only through nj, and through Whence 

But since P is homogeneous, the value of fiij is independent of the element of volume chosen, so that (15.99 ) becomes 

For this inequality to be satisfied, it is necessary and sufficient that i 22 i cc positive and that all the other minors, of both odd and even order, constructed on the principal diagonal of the determinant of the fjbij are positive or zero. 

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