On the relationship between principal fluctuations and stability coefficients in multicomponent systems

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Abstract
There is a univocal correspondence between each of the (n+2)! stability coefficients of an n‐component system and mean squared fluctuations of Gibbs‐space variables (entropy, volume, molecule number) in which the subsystem under study is defined through a single extensive Gibbs‐space variable (principal fluctuations). The relationship between principal fluctuations and stability coefficients [Eq. (53)] is derived in this paper starting from the usual expressions involving explicit calculation of the inverse of an (n+1)×(n+1) matrix. A general equation between higher order energy variations in fluctuating subsystems [Eq. (22)] is also derived. The relationship between principal fluctuations and stability coefficients yields, as particular cases, expressions which had been used previously for the limiting case of single‐component systems, or extended to solutions through heuristic arguments.