On mixing and metaequilibrium in nonextensive systems

Abstract

The analytical and computational studies of various isolated classical Hamiltonian systems including long-range interactions suggest that the N→∞ and t→∞ limits do not commute for entire classes of initial conditions. This is, for instance, the case for inertial planar rotators whenever the time evolution is started with the so-called waterbag distribution for velocities and full parallelism for the angles. For fixed N, after a transient, a long and robust anomalous plateau can emerge as time goes on whose velocity distribution is not the Maxwellian one; at later times, the system eventually crosses over onto the usual, Maxwellian distribution. The duration of the plateau diverges with N. This plateau can be considered as a metaequilibrium (or metastable) state, and its description might be in the realm of nonextensive statistical mechanics (for which the entropic index q≠1), whereas at later times the description is well done by the usual Boltzmann–Gibbs statistical mechanics ( q=1). The purpose of these lines is to present a scenario for the mixing properties (i.e., sensitivity to the initial conditions) which is consistent with the observations just mentioned.