Dynamical scenario for nonextensive statistical mechanics

Abstract

Statistical mechanics can only be ultimately justified in terms of microscopic dynamics (classical, quantum, relativistic, or any other). It is known that Boltzmann-Gibbs statistics is based on the hypothesis of exponential sensitivity to the initial conditions, mixing and ergodicity in Gibbs $Γ$-space. What are the corresponding hypothesis for nonextensive statistical mechanics? A scenario for answering such question is advanced, which naturally includes the {\it a priori} determination of the entropic index $q$, as well as its cause and manifestations, for say many-body Hamiltonian systems, in (i) sensitivity to the initial conditions in Gibbs $Γ$-space, (ii) relaxation of macroscopic quantities towards their values in anomalous stationary states that differ from the usual thermal equilibrium (e.g., in some classes of metastable or quasi-stationary states), and (iii) energy distribution in the $Γ$-space for the same anomalous stationary states.

Invited paper at the Second Sardinian International Conference on "News and Expectations in Thermostatistics" held in Villasimius (Cagliari)- Italy in 21-28 September 2003. 12 pages including 2 figures