The world according to Renyi: thermodynamics of fractal systems
Petr Jizba, Toshihico Arimitsu
Abstract
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.
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