The world according to Renyi: thermodynamics of fractal systems

We discuss a basic thermodynamic properties of systems with multifractal structure. This is possible by extending the notion of Gibbs-Shannon’s entropy into more general framework-Renyi’s information entropy. We show a connection of Renyi’s parameter q with the multifractal singularity spectrum f(α) and clarify a relationship with the Tsallis-Havrda-Charvat entropy. Finally, we generalize Hagedorn’s statistical theory and apply it to high-energy particle collisions.