  Starting from the BBGKY hierarchy, describing the kinetics of nonlinear
particle system, we obtain the relevant entropy and stationary distribution
function. Subsequently, by employing the Lorentz transformations we propose the
relativistic generalization of the exponential and logarithmic functions. The
related particle distribution and entropy represents the relativistic extension
of the classical Maxwell-Boltzmann distribution and of the Boltzmann entropy
respectively and define the statistical mechanics presented in [Phys. Rev. E
{\bf 66}, 056125 (2002)] and [Phys. Rev. E {\bf 72}, 036108 (2005). The
achievements of the present effort, support the idea that the experimentally
observed power law tailed statistical distributions in plasma physics, are
enforced by the relativistic microscopic particle dynamics.
