Critical fluctuations, intermittent dynamics and Tsallis statistics

TL;DR

This paper demonstrates that the dynamics of the order parameter at a thermal critical point follow Tsallis nonextensive statistics, linking critical fluctuations and intermittency through nonlinear map dynamics.

Contribution

It establishes a connection between critical phenomena and nonextensive Tsallis statistics via intermittent nonlinear map dynamics.

Findings

Critical fluctuations are described by intermittent nonlinear maps.

Intermittency near tangent bifurcations obeys nonextensive statistics.

The results imply a new understanding of stationary states at critical points.

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