  In special relativity the mathematical expressions, defining physical
observables as the momentum, the energy etc, emerge as one parameter (light
speed) continuous deformations of the corresponding ones of the classical
physics. Here, we show that the special relativity imposes a proper one
parameter continuous deformation also to the expression of the classical
Boltzmann-Gibbs-Shannon entropy. The obtained relativistic entropy permits to
construct a coherent and selfconsistent relativistic statistical theory [Phys.
Rev. E {\bf 66}, 056125 (2002); Phys. Rev. E {\bf 72}, 036108 (2005)],
preserving the main features (maximum entropy principle, thermodynamic
stability, Lesche stability, continuity, symmetry, expansivity, decisivity,
etc.) of the classical statistical theory, which is recovered in the classical
limit. The predicted distribution function is a one-parameter continuous
deformation of the classical Maxwell-Boltzmann distribution and has a simple
analytic form, showing power law tails in accordance with the experimental
evidence.
