Incidence of nonextensive thermodynamics in temporal scaling at Feigenbaum points

TL;DR

This paper examines the potential relevance of nonextensive thermodynamics, specifically q-statistics, to the dynamics at Feigenbaum points, challenging previous claims that found no connection.

Contribution

The authors clarify misconceptions and provide evidence supporting the applicability of nonextensive thermodynamics to Feigenbaum attractors.

Findings

Nonextensive thermodynamics can describe temporal scaling at Feigenbaum points.

Previous claims against q-statistics applicability are challenged and refuted.

The study aligns recent developments with the potential usefulness of generalized statistics.

Abstract

Recently, in Phys. Rev. Lett. 95, 140601 (2005), P. Grassberger addresses the interesting issue of the applicability of q-statistics to the renowned Feigenbaum attractor. He concludes there is no genuine connection between the dynamics at the critical attractor and the generalized statistics and argues against its usefulness and correctness. Yet, several points are not in line with our current knowledge, nor are his interpretations. We refer here only to the dynamics on the attractor to point out that a correct reading of recent developments invalidates his basic claim.