Abstract
The present paper is devoted to the relativistic statistical theory, introduced in Phys. Rev. E, 66 (2002) 056125 and Phys. Rev. E, 72 (2005) 036108, predicting the particle distribution function p(E)=expκ(−β[E−μ]) with 
and κ2<1. This, experimentally observed, relativistic distribution, at low energies behaves as the exponential, Maxwell-Boltzmann classical distribution, while at high energies presents power-law tails. Here, we obtain the evolution equation, conducting asymptotically to the above distribution, by using a new deductive procedure, starting from the relativistic BBGKY hierarchy and by employing the relativistic molecular chaos hypothesis.