A possible correction of the Saha curve for non-equilibrium states

It is widely known that the Saha equation is not suitable for describing plasmas out of thermodynamic equilibrium. The primordial hydrogen recombination plasma is an example of this. In this work, we propose a theoretical modification to the standard Saha curve motivated by Tsallis statistics. In particular, we explore the possibility that a time-dependent q -parameter may serve as an effective proxy for the evolving thermodynamic conditions during recombination, especially considering that hydrogen recombination occurs from excited states. Within this framework, the q -parameter could be interpreted as encoding departures from equilibrium and could play the role of effective time-dependent temperature. This indicates that the time evolution of the q -parameter could provide a phenomenological mechanism for incorporating non-equilibrium effects into the recombination history. Our findings suggest that the Tsallis parameterization provides an alternative path to fit the distribution of free electrons by using an effective temperature. The implications of this approach might go beyond its immediate applications, as the Saha equation is widely used in various scientific fields like astrophysics, cosmology, plasma physics, and condensed matter physics.