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13 pages, January 2009, arXiv -th- ph preprint

Abstract:

The paper shows that the special relativity laws and the maximum entropy principle suggest a relativistic generalization of both the two-particle correlation function and the corresponding entropy. A fully relativistic Boltzmann equation is presented which obeys the H-theorem and predicts a stationary stable distribution, presenting power-law tails in the high energy region. The resulting relativistic kinetic theory preserves the main features of the classical kinetics, which recovers in the limit of c tending to infinity. In experimental high energy physics, the power law tailed probability distributions functions, have been observed systematically in plasmas, cosmic rays, particle production processes, etc. A mechanism, frequently used to explain the occurrence of non exponential distributions, is based on certain non-linear evolution equations, mainly considered in the Fokker-Planck picture but recently also in the Boltzmann picture. Author's introduction to the subject: "Clearly, the correctness of the analytic expression of a given distribution, used to describe a statistical system, is strongly related to the validity of its generating mechanism. The classical Boltzmann equation, due to the particular form of the two-particle correlation function, present in the collisional integral, fixes uniquely the entropy of the system, which turns out to be Boltzmann-Gibbs-Shannon entropy. The latter entropy imposes the exponential form to the probability distribution function, emerging as the stationary and stable solution of the equation. In the ordinary relativistic Boltzmann equation, some standard generalizations, with respect its classical version, imposed by the special relativity, are customarily performed. The only ingredient of the equation, which tacitely remains in its original classical form, is the two-particle correlation function, and this fact imposes that also the relativistic kinetics is governed by the classical Boltzmann-Gibbs-Shannon entropy. Indeed the ordinary relativistic Boltzmann equation admits as stationary stable distribution, the exponential Juttner distribution." free online downloads at: http://arxiv.org/PS_cache/arxiv/pdf/0901/0901.1058v1.pdf

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Open access and free online downloads at: http://arxiv.org/PS_cache/arxiv/pdf/0901/0901.1058v1.pdf

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