# Relativistic kinetics and power-law tailed distributions

Source: [Relativistic kinetics and power-law tailed distributions](<https://www.sota2.com/research/paper/68fa29e41e209131ce83863a>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T13:11:56.181Z

Authors: G. Kaniadakis

Published: 2010-12-17T15:10:29.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1012.3903>)

[PDF](<https://arxiv.org/pdf/1012.3903.pdf>)