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

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dc.creatorSilva, R.
dc.date2006-11-29
dc.date.accessioned2026-07-07T07:44:25Z
dc.date.available2026-07-07T07:44:25Z
dc.descriptionWe have investigated the proof of the $H$ theorem within a manifestly covariant approach by considering the relativistic statistical theory developed in [G. Kaniadakis, Phy. Rev. E {\bf 66}, 056125, 2002; {\it ibid.} {\bf 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., $f(x,p)\propto (\sqrt{1+ κ^2θ^2}+κθ)^{1/κ}\equiv\exp_κθ$, 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 $κ\to 0$.
dc.description7 pages; to be published in EPJB
dc.identifierhttps://arxiv.org/abs/cond-mat/0611753
dc.identifierhttp://arxiv.org/abs/cond-mat/0611753
dc.identifierEur. Phys. J. B 54, 499 (2006)
dc.identifierdoi:10.1140/epjb/e2007-00029-3
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123187
dc.subjectStatistical Mechanics
dc.titleThe relativistic statistical theory and Kaniadakis entropy: an approach through a molecular chaos hypothesis
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