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., \(f(x,p)\propto (\sqrt{1+ \kappa^2\theta^2}+\kappa\theta)^{1/\kappa}\equiv\exp_\kappa\theta\), with θ=α(x)+βμpμ, where α(x) is a scalar, βμ is a four-vector, and pμ 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 Fμν. All standard results are readly recovered in the particular limit κ→0.
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Silva, R. The relativistic statistical theory and Kaniadakis entropy: an approach through a molecular chaos hypothesis. Eur. Phys. J. B 54, 499–502 (2006). https://doi.org/10.1140/epjb/e2007-00029-3
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DOI: https://doi.org/10.1140/epjb/e2007-00029-3