A Dynamic Approach to the Thermodynamics of Superdiffusion
  We address the problem of relating thermodynamics to mechanics in the case of microscopic dynamics without a finite time scale. The solution is obtained by expressing the Tsallis entropic index q as a function of the Levy index alpha, and using dynamical rather than probabilistic arguments. 
Marco Buiatti (1), Paolo Grigolini (1,2,3) and Anna Montagnini (1)   ((1) Istituto di Biofisica del Consiglio Nazionale dell...