Gamow Temperature in Tsallis and Kaniadakis Statistics

TL;DR

The paper investigates how non-extensive statistics alter Gamow's quantum-tunneling-based fusion threshold in stellar gases. By applying Tsallis and Kaniadakis frameworks, it derives generalized equipartition relations that modify the Gamow temperature and the associated thermal length scale, yielding $T_q = \frac{5-3q}{2} T$ with $r_{0q}^T = \frac{5-3q}{2} r_0^T$ and $T_\kappa = T/\gamma_\kappa$ with $r_{0\kappa}^T = r_0^T/\gamma_\kappa$, recovering MBG in the limits $q\to1$ and $\kappa\to0$. The results show $T_\kappa \le T$ for Kaniadakis statistics and that $T_q$ can be either below or above $T$ for Tsallis statistics, with analogous shifts in the length scales. This links non-extensive thermodynamics to stellar fusion thresholds and suggests that observed stellar temperatures could constrain the non-extensive parameters $q$ or $\kappa$, pending further theoretical development and observational fitting.

Abstract

Relying on the quantum tunnelling concept and Maxwell-Boltzmann-Gibbs statistics, Gamow shows that the star-burning process happens at temperatures comparable to a critical value, called the Gamow temperature ({\tt T}) and less than the prediction of the classical framework. In order to highlight the role of the equipartition theorem in the Gamow argument, a thermal length scale is defined, and then the effects of non-extensivity on the Gamow temperature have been investigated by focusing on the Tsallis and Kaniadakis statistics. The results attest that while the Gamow temperature decreases in the framework of Kaniadakis statistics, it can be bigger or smaller than {\tt T} when Tsallis statistics are employed.