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

摘要

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. power law generalization of the exponential Juttner distribution, e. g., f(x, p) proportional to (root 1 +kappa(2)theta(2) +kappa theta)(1/kappa) = exp(kappa) theta, with theta = alpha(x) + beta(mu)p(mu), where alpha(x) is a scalar, beta(mu) is a four-vector, and p(mu) is the four-momentum. As a simple example, we calculate the relativistic. power law for a dilute charged gas under the action of an electromagnetic field F-mu nu. All standard results are readly recovered in the particular limit kappa --> 0.