# Non-Gaussian thermostatistical considerations upon the Saha equation

## TL;DR

This paper extends the Saha equation using non-Gaussian thermostatistics, specifically Tsallis and Kaniadakis formalisms, to better model complex astrophysical ionization processes and introduces new chemical potentials.

## Contribution

It introduces two non-Gaussian generalizations of the Saha equation based on Tsallis and Kaniadakis statistics, demonstrating their effectiveness in astrophysical ionization systems.

## Key findings

- Derived new $q$-potentials and their graphical regions.
- Analyzed asymptotic behavior of the $q$-potential.
- Extended the formalism to complex atoms and pair production reactions.

## Abstract

The Saha equation provides the relation between two consecutive ionization state populations, like the Maxwell-Boltzmann velocity distribution of the atoms in a gas ensemble. Saha equation can also consider the partitions functions for both states and its main application is in stellar astrophysics population statistics. This paper presents two non-Gaussian thermostatistical generalizations for the Saha equation: the first one towards the Tsallis nonextensive $q$-entropy and the other one is based upon Kaniadakis $\kappa$-statistics. Both thermostatistical formalisms are very successful when used in several complex astrophysical statistical systems and we have demonstrated here that they work also in Saha's ionization distribution. We have obtained new chemical $q$-potentials and their respective graphical regions with a well defined boundary that separated the two symmetric intervals for the $q$-potentials. The asymptotic behavior of the $q$-potential was also discussed. Besides the proton-electron, we have also investigated the complex atoms and pair production ionization reactions.