The nonextensive parameter and Tsallis distribution for self-gravitating systems

TL;DR

This paper explores the role of the nonextensive parameter q and Tsallis distribution in describing self-gravitating systems, linking q to temperature gradients and gravitational potential within a nonextensive statistical framework.

Contribution

It derives a mathematical expression for q based on generalized Boltzmann equation and Maxwellian distribution, providing insights into non-equilibrium, long-range interacting systems.

Findings

q differs from unity due to temperature gradients and gravitational potential

Tsallis statistics are suitable for inhomogeneous, nonequilibrium systems

Provides a theoretical foundation for nonextensive thermodynamics in astrophysics

Abstract

The properties of the nonextensive parameter q and the Tsallis distribution for self-gravitating systems are studied. A mathematical expression of q is deduced based on the generalized Boltzmann equation, the q-H theorem and the generalized Maxwellian q-velocity distribution in the framework of Tsallis statistics. We obtain a clear understanding of the physics of q different from unity with regard to the temperature gradient and the gravitational potential of the self-gravitating systems. It is suggested that the Tsallis statistics could be statistics suitable for describing the nonequilibrium systems with inhomogeneous temperature and the long-range interactions.