On the computation of the entropy for dissipative maps at the edge of chaos using non-extensive statistical mechanics

TL;DR

This paper examines the use of Tsallis' non-extensive statistical mechanics to describe dissipative maps at the edge of chaos, highlighting potential contradictions in the current theoretical framework through analytical and numerical analysis.

Contribution

The paper provides analytical and numerical insights that challenge the prevailing view of non-extensive mechanics accurately describing edge-of-chaos dynamics.

Findings

Power-law behavior confirmed in some cases

Contradictions found in the theoretical predictions

Analytical considerations suggest limitations of current models

Abstract

Tsallis' non-extensive statistical mechanics is claimed to be the correct tool to describe the behaviour of low-dimensional dissipative maps at the edge of chaos. Indeed, many different approaches confirm that, for those systems, the evolution is governed by power-laws, not exponential, trends; this coincides with predictions from generalized thermostatistics. In this work, however, we present some analytical considerations, supported also by some simple numerical examples, suggesting the existence of contradictions within this picture.