Eur. Phys. J. B 54, 499-502 (2006)
https://doi.org/10.1140/epjb/e2007-00029-3

The relativistic statistical theory and Kaniadakis entropy: an approach through a molecular chaos hypothesis

Universidade do Estado do Rio Grande do Norte, 59610-210 Mossoró, RN, Brazil and Observatrio Nacional, Rua Gal. Jos Cristino 77, 20921-400 Rio de Janeiro, RJ, Brazil

Corresponding author: ^a raimundosilva@uern.br

Received: 28 April 2006
Revised: 3 November 2006
Published online: 3 February 2007

Abstract

We have investigated the proof of the H theorem within a manifestly covariant approach by considering the relativistic statistical theory developed in [G. Kaniadakis, Phys. Rev. E 66, 056125 (2002); G. Kaniadakis, Phys. Rev. E 72, 036108 (2005)]. As it happens in the nonrelativistic limit, the molecular chaos hypothesis is slightly extended within the Kaniadakis formalism. It is shown that the collisional equilibrium states (null entropy source term) are described by a κ power law generalization of the exponential Juttner distribution, e.g., , with θ=α(x)+β_μp^μ, where α(x) is a scalar, β_μ is a four-vector, and p^μ is the four-momentum. As a simple example, we calculate the relativistic κ power law for a dilute charged gas under the action of an electromagnetic field F^μν. All standard results are readly recovered in the particular limit κ→0.