A remarkable feature of high energy collisions is the power-law behavior of the transverse momentum distributions, p_T. Although at the high momentum sector this can be explained in terms of perturbative QCD, the low momentum sector can be described only by the assumption of a thermodynamically equilibrated system formed in the collision.
It has been shown that when Tsallis statistics is used, the well-known Hagedorn self-consistent thermodynamics, now extended with the non extensive features, can describe the experimental data with only two free parameters that are independent of the collision energy and of the observed particle mass, namely, the critical temperature, T, and the entropic index, q, which appears in Tsallis statistics.
Recently it was shown that the non extensive behavior of the hadronic systems can be related to a fractal structure in its thermodynamical functions. The fractal dimension is determined by those two parameters of the Tsallis statistics and, suprisingly, is in accordance with the fractal dimension obtained from the analysis of intermittance in the high energy distributions.
In this talk we present an overview on the developments of the non extensive self-consistent thermodynamics applied for high energy collisions and discuss possible implications in the investigation of non-perturbative QCD.