Relativistic kinetics and power-law tailed distributions

TL;DR

This paper develops a relativistic kinetic theory that derives a distribution function with exponential behavior at low energies and power-law tails at high energies, aligning with experimental observations.

Contribution

It introduces a new deductive method from the relativistic BBGKY hierarchy to derive the relativistic distribution with power-law tails.

Findings

Distribution behaves as Maxwell-Boltzmann at low energies

Distribution exhibits power-law tails at high energies

Derived evolution equation asymptotically approaches the relativistic distribution

Abstract

The present paper is devoted to the relativistic statistical theory, introduced in Phys. Rev. E {\bf 66} (2002) 056125 and Phys. Rev. E {\bf 72} (2005) 036108, predicting the particle distribution function $p(E)= \exp_{\kappa} (-\beta[E-\mu])$ with $\exp_{\kappa}(x)=(\sqrt{1+ \kappa^2 x^2}+\kappa x)^{1/\kappa}$, and $\kappa^2<1$. This, experimentally observed, relativistic distribution, at low energies behaves as the exponential, Maxwell-Boltzmann classical distribution, while at high energies presents power law tails. Here, we obtain the evolution equation, conducting asymptotically to the above distribution, by using a new deductive procedure, starting from the relativistic BBGKY hierarchy and by employing the relativistic molecular chaos hypothesis.