A Maxwellian Path to the q-Nonextensive Velocity Distribution Function

TL;DR

This paper generalizes Maxwell's velocity distribution for gases using Tsallis's nonextensive q-statistics and applies it to derive the q-Doppler broadening of spectral lines, expanding the theoretical framework of statistical mechanics.

Contribution

It introduces a generalized velocity distribution function based on nonextensive q-statistics and applies it to spectral line broadening phenomena.

Findings

Derived the q-velocity distribution function for dilute gases.

Obtained the q-Doppler broadening formula for spectral lines.

Extended Maxwell's classical distribution within a nonextensive statistical framework.

Abstract

Maxwell's first derivation of the equilibrium distribution function for a dilute gas is generalized in the spirit of the nonextensive q-statistics proposed by Tsallis. As an application, the q-Doppler broadening of spectral lines due to the random thermal motion of the radiating atoms is derived.