A Maxwellian Path to the q-Nonextensive Velocity Distribution Function

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. 05.45.+b; 05.20.-y; 05.90.+m Typeset using REVTEX ∗[email protected] †[email protected] ‡[email protected] 1 It is widely known that the thermodynamical or statistical description of nonextensive systems demand a generalization of the usual Boltzmann-Gibbs thermostatistics [1–3]. A few important examples of physical systems or processes where the standard approach seems to be inadequate are self-gravitating systems, some kinds of plasma turbulence, and selforganized criticality. The standard Boltzmann-Gibbs approach is based on the extensive entropy measure