Thermofractal Dynamics in the Multisource Thermal Model: A Unified Approach to Multiparticle Production

Abstract

The empirical success of non-extensive Tsallis statistics and multisource thermal models in describing transverse-momentum (pT ) spectra and rapidity distributions in high-energy relativistic collisions highlights a deep connection between expansion geometry, non-extensive thermodynamics, and QCD dynamics. In this work, we establish a theoretical framework showing that the thermofractal structure of QCD phase space provides a direct microscopic foundation for the multisource thermal model. By exploiting the Euler integral representation of non-extensive statistical factors, we demonstrate that a single thermofractal emission source generating q-exponential distributions is mathematically equivalent to a continuous superposition of local Boltzmann thermal sources whose temperature fluctuations follow an inverse-Gamma distribution. Furthermore, we prove that multi- component phenomenological fits with discrete source temperatures represent the exact, optimal Gauss-Laguerre quadrature discretisation of this underlying continuous thermofractal field. We show how this continuous field constrains the temperature parameter space in multisource formulations, matches pQCD hard-scattering power-law asymptotics, and provides a robust vacuum baseline for medium-induced jet quenching and nuclear modification factor (RAA ) calculations.