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

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 <Emphasis Type="Bold">66, 056125 (2002); G. Kaniadakis, Phys. Rev. E <Emphasis Type="Bold">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., <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$f(x,p)\propto (\sqrt{1+ \kappa^2\theta^2}+\kappa\theta)^{1/\kappa}\equiv\exp_\kappa\theta$</Equati onSource> </InlineEquation>, with θ=α(x)+β<Subscript>μ</Subscript>p<Superscript>μ</Superscript>, where α(x) is a scalar, β<Subscript>μ</Subscript> is a four-vector, and p<Superscript>μ</Superscript> 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<Superscript>μν</Superscript>. All standard results are readly recovered in the particular limit κ→0. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006