Abstract composition rule for relativistic kinetic energy in the thermodynamical limit

KFKI Research Institute for Particle and Nuclear Physics - P.O. Box 49, H-1525 Budapest, Hungary, EU

Corresponding author: tsbiro@mail.kfki.hu

Received: 26 September 2008
Accepted: 28 October 2008

Abstract

We demonstrate by simple mathematical considerations that a power-lawtailed distribution in the kinetic energy of relativistic particles can be a limiting distribution seen in relativistic heavy-ion experiments. We prove that the infinite repetition of an arbitrary composition rule on an infinitesimal amount leads to a rule with a formal logarithm. As a consequence the stationary distribution of energy in the thermodynamical limit follows the composed function of the Boltzmann-Gibbs exponential with this formal logarithm. In particular, interactions described as solely functions of the relative four-momentum squared lead to kinetic energy distributions of the Tsallis-Pareto (cut power law) form in the high-energy limit.