Relativity, nonextensivity, and extended power law distributions

Details Relativity, nonextensivity, and extended power law distributions Relativity, nonextensivity, and extended power law distributions

2005-10-07

arxiv.org/abs/cond-mat/0510201v1

Phys.Rev. E72 (2005) 057101

Physics

Condensed Matter

Statistical Mechanics

Accepted for publication in PRE

Scientific paper

10.1103/PhysRevE.72.057101

A proof of the relativistic $H$-theorem by including nonextensive effects is given. As it happens in the nonrelativistic limit, the molecular chaos hypothesis advanced by Boltzmann does not remain valid, and the second law of thermodynamics combined with a duality transformation implies that the q-parameter lies on the interval [0,2]. It is also proved that the collisional equilibrium states (null entropy source term) are described by the relativistic $q$-power law extension of the exponential Juttner distribution which reduces, in the nonrelativistic domain, to the Tsallis power law function. As a simple illustration of the basic approach, we derive the relativistic nonextensive equilibrium distribution for a dilute charged gas under the action of an electromagnetic field $F^{{\mu\nu}}$. Such results reduce to the standard ones in the extensive limit, thereby showing that the nonextensive entropic framework can be harmonized with the space-time ideas contained in the special relativity theory.

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