On mixing and metaequilibrium in nonextensive systems

Constantino Tsallis

Physica A: Statistical Mechanics and its Applications, 2001, vol. 302, issue 1, 187-192

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.

Keywords: Nonextensive statistics; Metaequilibrium; Nonmaxwellian distributions; Power laws (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:302:y:2001:i:1:p:187-192

DOI: 10.1016/S0378-4371(01)00463-0

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