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Abstract: It is well known that the particular form of the two-particle correlationfunction, in the collisional integral of the classical Boltzmman equation, fixunivocally the entropy of the system, which turn out to be theBoltzmann-Gibbs-Shannon entropy.In the ordinary relativistic Boltzmann equation, some standardgeneralizations, with respect its classical version, imposed by the specialrelativity, are customarily performed. The only ingredient of the equation,which tacitly remains in its original classical form, is the two-particlecorrelation function, and this fact imposes that also the relativistic kineticsis governed by the Boltzmann-Gibbs-Shannon entropy. Indeed the ordinaryrelativistic Boltzmann equation admits as stationary stable distribution, theexponential Juttner distribution.Here, we show that the special relativity laws and the maximum entropyprinciple, suggest a relativistic generalization also of the two-particlecorrelation function and then of the entropy. The so obtained, fullyrelativistic Boltzmann equation, obeys the H-theorem and predicts a stationarystable distribution, presenting power-law tails in the high energy region. Theensued relativistic kinetic theory preserves the main features of the classicalkinetics, which recovers in the $c \to \infty$ limit.

Author: G. Kaniadakis


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