Non-Gaussian statistics, maxwellian derivation and stellar polytropes

TL;DR

This paper explores non-Gaussian statistics by extending Maxwell's derivation within Kaniadakis statistics and investigates the relationship between the entropic parameter and stellar polytrope index, comparing it with Tsallis framework results.

Contribution

It extends Maxwell's derivation to Kaniadakis statistics and establishes a relation between the entropic parameter and stellar polytrope index, comparing with Tsallis statistics.

Findings

Extended Maxwell's derivation in Kaniadakis framework

Derived relation between $ppa$ and stellar polytrope index $n$

Compared Kaniadakis and Tsallis relations for $n(ppa)$ and $n(q)$

Abstract

In this letter we discuss the Non-gaussian statistics considering two aspects. In the first, we show that the Maxwell's first derivation of the stationary distribution function for a dilute gas can be extended in the context of Kaniadakis statistics. The second one, by investigating the stellar system, we study the Kaniadakis analytical relation between the entropic parameter $\kappa$ and stellar polytrope index $n$. We compare also the Kaniadakis relation $n=n(\kappa)$ with $n=n(q)$ proposed in the Tsallis framework.