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 q(mix) less than or equal to 1) and equilibration (characterized by the entropic index q(eq) greater than or equal to 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 q(mix) = q(eq) = 1 particular case. (C) 2002 Elsevier Science B.V. All rights reserved.