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Main Authors: Cao, Wenfu, Chen, Siyan, Zhang, Hongsheng
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2601.18422
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author Cao, Wenfu
Chen, Siyan
Zhang, Hongsheng
author_facet Cao, Wenfu
Chen, Siyan
Zhang, Hongsheng
contents We propose a novel chaos indicator -- time-reversed Shannon entropy (TRSE) -- that leverages the interplay between time-reversal symmetry breaking and information entropy in curved spacetimes. By quantifying statistical discrepancies between forward and backward temporal evolution of particle orbits, TRSE robustly distinguishes chaotic from regular dynamics in non-integrable systems. In contrast, integrable systems exhibit stable, symmetric probability distributions preserved by conserved quantities such as the Carter constant. We validate the method through high-precision numerical simulations in both Kerr and Schwarzschild-Melvin black hole geometries, evolving trajectories forward and backward in time. Furthermore, we refine our previously introduced particle-pair mutual information (MIPP) and perform comprehensive parameter-space scans, revealing a strong quantitative agreement between MIPP and TRSE. The two indicators emerge as complementary probes of chaos: TRSE captures symmetry breaking in orbital evolution, while MIPP measures statistical correlations. Together, they establish a unified framework for diagnosing chaos in general relativistic systems, paving a new path to understand the fundamental nature of chaos in non-integrable systems.
format Preprint
id arxiv_https___arxiv_org_abs_2601_18422
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Time-reversed Shannon entropy as a chaos indicator for non-integrable systems
Cao, Wenfu
Chen, Siyan
Zhang, Hongsheng
General Relativity and Quantum Cosmology
We propose a novel chaos indicator -- time-reversed Shannon entropy (TRSE) -- that leverages the interplay between time-reversal symmetry breaking and information entropy in curved spacetimes. By quantifying statistical discrepancies between forward and backward temporal evolution of particle orbits, TRSE robustly distinguishes chaotic from regular dynamics in non-integrable systems. In contrast, integrable systems exhibit stable, symmetric probability distributions preserved by conserved quantities such as the Carter constant. We validate the method through high-precision numerical simulations in both Kerr and Schwarzschild-Melvin black hole geometries, evolving trajectories forward and backward in time. Furthermore, we refine our previously introduced particle-pair mutual information (MIPP) and perform comprehensive parameter-space scans, revealing a strong quantitative agreement between MIPP and TRSE. The two indicators emerge as complementary probes of chaos: TRSE captures symmetry breaking in orbital evolution, while MIPP measures statistical correlations. Together, they establish a unified framework for diagnosing chaos in general relativistic systems, paving a new path to understand the fundamental nature of chaos in non-integrable systems.
title Time-reversed Shannon entropy as a chaos indicator for non-integrable systems
topic General Relativity and Quantum Cosmology
url https://arxiv.org/abs/2601.18422