Gibbs phase rule

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Gibbs phase rule

[′gibz ′fāz ‚rül]

(physical chemistry)

A relationship used to determine the number of state variables F, usually chosen from among temperature, pressure, and species composition in each phase, which must be specified to fix the thermodynamic state of a system in equilibrium: F = C-P-M +2, where C is the number of chemical species presented at equilibrium, P is the number of phases, and M is the number of independent chemical reactions. Also known as Gibbs rule; phase rule.

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In general, correct solutions to the phase-mapping problem should follow the Gibbs phase rule, which specifies that the number of observed phases at a given chemical composition is no more than the number of chemical elements [N.sub.el]:

As a novel routine, we apply the Gibbs phase rule by first solving the relaxed problem, then choose the best values to set to zero in H, and then refine the solution by applying the update rules until convergence.

We tested NMF (implemented as AgileFD with M = 1), AgileFD, AgileFD with sparsity regularization (AgileFD-Sp), AgileFD with sparsity and the Gibbs phase rule enforced (AgileFD-Sp-Gibbs), and CombiFD (Ermon et.