TL;DR
This paper offers a geometric, model-independent explanation for why Tsallis entropy effectively describes systems with weak chaos, characterized by zero Lyapunov exponents, based on properties of a deformation map.
Contribution
It introduces a novel geometric argument linking Tsallis entropy to weak chaos, independent of specific models, aligning with existing empirical findings.
Findings
Tsallis entropy models systems with vanishing Lyapunov exponents
The geometric argument aligns with known results on weak chaos
Provides a new perspective on entropy and dynamical systems
Abstract
We present a geometric, model-independent, argument that aims to explain why the Tsallis entropy describes systems exhibiting "weak chaos", namely systems whose underlying dynamics has vanishing largest Lyapunov exponent. Our argument relies on properties of a deformation map of the reals induced by the Tsallis entropy, and its conclusion agrees with all currently known results.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.