Screen chaotic motion by Shannon entropy in curved spacetimes

TL;DR

This paper introduces Shannon entropy as a new, intuitive measure to distinguish chaotic from regular orbits in curved spacetimes, showing it aligns well with traditional chaos indicators and offers new insights into thermodynamics and dynamics.

Contribution

The paper presents a novel application of Shannon entropy to characterize chaotic motion in curved spacetimes, providing a clear and theoretically sound alternative to existing methods.

Findings

Shannon entropy correlates well with traditional chaos indicators.

It effectively distinguishes between chaotic and regular orbits.

Potential to define entropy for a single orbit and explore thermodynamics-dynamics relations.

Abstract

We find a novel characteristic for chaotic motion by introducing Shannon entropy for periodic orbits, quasiperiodic orbits, and chaotic orbits.We compare our approach with the previous methods including Poincar\'{e} Section, Lyapunov exponent, Fast Lyapunov Indicator, Recurrence plots(Rps), and Fast Fourier Transform(FFT) for orbits around black hole immersed in magnetic fields, and show that they agree with each other quite well. The approach of Shannon entropy is intuitively clear, and theoretically reasonable since it becomes larger and larger form a periodic orbit to chaotic orbit. We demonstrate that Shannon entropy can be a powerful probe to distinguish between chaotic and regular orbits in different spacetimes, and reversely may lead to a new road to define the entropy for a single orbit in phase space, and to find more fundamental relations between thermodynamics and dynamics.