  The role played by non-extensive thermodynamics in physical systems has been
under intense debate for the last decades. Some possible mechanisms that could
give rise to non-extensive statistics have been formulated along the last few
years, in particular the existence of a fractal structure in thermodynamic
functions for hadronic systems. We investigate the properties of such fractal
thermodynamical systems, in particular the fractal scale invariance is
discussed in terms of the Callan-Symanzik~equation. Finally, we propose a
diagrammatic method for calculations of relevant quantities.
