2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/219411We demonstrate by simple mathematical considerations that a power-law tailed 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.Submitted to Europhysics Letters. LaTeX, 3 eps figuresNuclear TheoryStatistical Mechanicstext