Physical origin of the power-law tailed statistical distributions

TL;DR

This paper derives a relativistic statistical mechanics framework from the BBGKY hierarchy, explaining power-law tailed distributions in plasma physics as a consequence of relativistic particle dynamics.

Contribution

It introduces a relativistic extension of classical statistical functions, linking microscopic relativistic effects to observed power-law distributions in plasma.

Findings

Relativistic generalization of exponential and logarithmic functions.

Derivation of relativistic Maxwell-Boltzmann distribution and entropy.

Support for relativistic dynamics explaining power-law tails in plasma distributions.

Abstract

Starting from the BBGKY hierarchy, describing the kinetics of nonlinear particle system, we obtain the relevant entropy and stationary distribution function. Subsequently, by employing the Lorentz transformations we propose the relativistic generalization of the exponential and logarithmic functions. The related particle distribution and entropy represents the relativistic extension of the classical Maxwell-Boltzmann distribution and of the Boltzmann entropy respectively and define the statistical mechanics presented in [Phys. Rev. E {\bf 66}, 056125 (2002)] and [Phys. Rev. E {\bf 72}, 036108 (2005). The achievements of the present effort, support the idea that the experimentally observed power law tailed statistical distributions in plasma physics, are enforced by the relativistic microscopic particle dynamics.