Thermodynamics with fractal structure, Tsallis statistics and hadrons

A system presenting fractal structure in its thermodynamical functions is introduced, and it is shown that Tsallis statistics is the correct framework for describing the thermodynamical aspects of such fractal. Its Haussdorf dimension and its Lipshitz-H"older exponent are determined in terms of the entropic index $q$. The connections with the intermittency in experimental data is discussed. The thermodynamical aspects of the thermofractal is related to the microscopic interaction of its components through the S-matrix.