Critical fluctuations, intermittent dynamics and Tsallis statistics

Abstract

It is pointed out that the dynamics of the order parameter at a thermal critical point obeys the precepts of the nonextensive Tsallis statistics. We arrive at this conclusion by putting together two well-defined statistical-mechanical developments. The first is that critical fluctuations are correctly described by the dynamics of an intermittent nonlinear map. The second is that intermittency in the neighborhood of a tangent bifurcation in such map rigorously obeys nonextensive statistics. We comment on the implications of this result. Key words: critical fluctuations, intermittency, nonextensive statistics, anomalous stationary states

Contribution to the proceedings of International Workshop on Trends and Perspectives on Extensive and Non-Extensive Statistical Mechanics (q-60), Angra dos Reis, Brazil, 17-21/11/2003. Submitted to Physica A

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• Generalized Statistical Mechanics at the Onset of Chaos
• Intermittency at critical transitions and aging dynamics at edge of chaos
• Manifestations of the onset of chaos in condensed matter and complex systems