Nonuniqueness of the two-temperature Saha equation and related considerations

The present paper contains considerations relative to the long debated thermodynamic derivation of two-temperature Saha equations. The main focus of our discourse is on the dependence of the multitemperature equilibrium conditions on the constraints imposed on the thermodynamic system. We also examine the following key issues related to that dependence: correspondence between constraints and equilibrium-equation forms that have appeared in the literature; presumed dominance of the free-electron translational temperature in the two-temperature expression of the equilibrium constant of the ionization reaction A <--> A++e(-); disagreement between the derivation methods based on, respectively, the extended second law of classical thermodynamics and axiomatic thermodynamics; and plausibility of the existence of entropic constraints.