Abstract composition rule for relativistic kinetic energy in the thermodynamical limit

TL;DR

This paper shows that in relativistic heavy ion experiments, the energy distribution of particles tends to a power-law tail described by a formal logarithm, linking it to Tsallis-Pareto statistics in the thermodynamical limit.

Contribution

It introduces a mathematical framework connecting composition rules to stationary energy distributions, deriving Tsallis-Pareto forms from relativistic interactions.

Findings

Power-law tailed distributions emerge as thermodynamic limits.

Repetition of composition rules leads to a formal logarithm.

Relativistic interactions produce Tsallis-Pareto energy distributions.

Abstract

We 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.