Non-Gaussian thermostatistical considerations upon the Saha equation

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.

15 pages. Preprint format

References in corpus (4)

• Generalized entropy formalism and a new holographic dark energy model
• Tsallis and Kaniadakis statistics from a point of view of the holographic equipartition law
• Extended $\Lambda$CDM model
• q-Stirling's formula in Tsallis statistics

Cited by in corpus (5)

• The k-statistics approach to epidemiology
• New power-law tailed distributions emerging in $\kappa$-statistics
• Non-Gaussian Effects of the Saha's Ionization in the Early Universe
• A possible correction of the Saha curve for non-equilibrium states
• An outlier-resistant $\kappa$-generalized approach for robust physical parameter estimation