Relativistic kinetics and power-law tailed distributions

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.

5 two-column pages

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• Theoretical foundations and mathematical formalism of the power-law tailed statistical distributions
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• Physical origin of the power-law tailed statistical distributions
• Relativistic Roots of $\kappa$-Entropy
• Power-Law tailed statistical distributions and Lorentz transformations
• Kappa-deformed random-matrix theory based on Kaniadakis statistics