Hi Nick,
I am a complete novice in using Cantera. I was going through the National Combustion meetings 2019 (
https://github.com/Cantera/ncm-2019-materials) trying to feel my way around cantera when I found what might relate to your question. I am sorry if it is of no use to you but the section 01_cantera_basics.ipynb in the Jupyter notebook has the information below:
Method equilibrate invokes Cantera's chemical equilibrium solver, which uses an element potential method. The element potential method is one of a class of equivalent nonstoichiometric methods that all have the characteristic that the probelm reduces to solving a set of 𝑀 nonlinear algebraic equations, where 𝑀 is the number of elements (not species). The so-called stoichiometric methods, on the other hand (including the Gibbs minimization), require solving 𝐾 nonlinear equations, where 𝐾 is the number of species (usually 𝐾>>𝑀). See Smith and Missen's "Chemical Reaction Equilibrium Analysis" for more information on the various algorithms and their characteristics.
Regards,
Daniel