  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.
