Mixing and equilibration: protagonists in the scene of nonextensive statistical mechanics

After a brief review of the present status of nonextensive statistical mechanics, we present a conjectural scenario where mixing (characterized by the entropic index qmix 1) and equilibration (characterized by the entropic index qeq 1) play central and inter-related roles, and appear to determine a priori the values of the relevant indices of the formalism. Boltzmann–Gibbs statistical mechanics is recovered as the qmix=qeq=1 particular case.