The world according to Renyi: thermodynamics of fractal systems

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(\alpha) 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.

Comments: 8 LaTeX pages, Proc. of the International Symposium on Non-equilibrium and Nonlinear Dynamics in Nuclear and Other Finite Systems