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