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 firstname.lastname@example.org
Revised: 3 November 2006
Published online: 3 February 2007
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)+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.
PACS: 05.90.+m – Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems / 05.20.-y – Classical statistical mechanics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2007