Gamow Temperature in Tsallis and Kaniadakis Statistics

TL;DR

This paper investigates how non-extensive statistical frameworks like Tsallis and Kaniadakis modify the Gamow temperature, which is crucial for understanding star-burning processes, revealing that these frameworks can either increase or decrease the temperature compared to classical predictions.

Contribution

It introduces the effects of Tsallis and Kaniadakis statistics on the Gamow temperature, highlighting the impact of non-extensivity on stellar thermodynamics.

Findings

Kaniadakis statistics decrease the Gamow temperature.

Tsallis statistics can increase or decrease the Gamow temperature.

Results emphasize the role of non-extensive statistics in astrophysical processes.

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.