Hierarchical Decoupling of Informational and Energetic Channels in Dissipative Chaos: From Microscopic Tangles to Macroscopic Transport
Abstract
Characterizing deterministic chaos in driven dissipative systems presents a fundamental challenge: geometric methods detect topological horseshoes (hT > 0) without certifying physical measures, while macroscopic observables reduce multi-scale dynamics into low-dimensional indicators. We demonstrate that phase-space contraction structurally decouples the informational channel, governed by topological complexity and Kolmogorov-Sinai entropy (hKS), from the energetic channel governing macroscopic dissipation, power balance, and transport. We establish a three-tier hierarchical architecture bridging: (I) microscopic topology (invariant manifold tangles), (II) ergodic physical measures (metric entropy and Lyapunov spectra), and (III) macroscopic ensemble statistics (variance and transport flux). In the forced two-well Duffing oscillator, high-resolution numerical analyses reveal the origin of classical predictive failures: dense homoclinic tangles degenerate into non-retaining transient saddles (hT > 0, hKS = 0) collapsing to periodic sinks, whereas macroscopic chaos persists past primary homoclinic tangency via higher-order saddle relays. Generalizing to periodic-potential rotational systems shows that heteroclinic crossings and resonant Shapiro steps enforce geometric bounds on phase slips and transport. Structurally disentangling informational capacity from energetic realization connects geometric mechanics with non-equilibrium statistical observability, offering a new diagnostic framework for noise-induced instabilities in nonlinear systems.
Related
- Variational learning of energy-stable macroscopic flow equations from microscopic laws
- Effect of non-homogeneous non-magnetic Impurities in Superconductors: A comparison between Microscopic and Macroscopic theories
- Microscopic Bipartition and Macroscopic Symmetry in a Rényi Entanglement Ensemble
- Generalized reverberation theory in diffuse sound fields: Introducing mean residual free path for macroscopic and microscopic unification
- Early-age aggregation of alkali-activated slag: from microscopic relaxation to macroscopic elasticity, and the effect of PCE
BibTeX
@misc{hikihara2026hierarchical,
title = {{Hierarchical Decoupling of Informational and Energetic Channels in Dissipative Chaos: From Microscopic Tangles to Macroscopic Transport}},
author = {Takashi Hikihara},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2608.19620},
eprint = {2608.19620},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.19620},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Hierarchical Decoupling of Informational and Energetic Channels in Dissipative Chaos: From Microscopic Tangles to Macroscopic Transport
AU - Takashi Hikihara
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2608.19620
UR - https://arxiv.org/abs/2608.19620
AB - Characterizing deterministic chaos in driven dissipative systems presents a fundamental challenge: geometric methods detect topological horseshoes (h_T > 0) without certifying physical measures, while macroscopic observables reduce multi-scale dynamics into low-dimensional indicators. We demonstrate that phase-space contraction structurally decouples the informational channel, governed by topological complexity and Kolmogorov-Sinai entropy (h_KS), from the energetic channel governing macroscopic dissipation, power balance, and transport. We establish a three-tier hierarchical architecture bridging: (I) microscopic topology (invariant manifold tangles), (II) ergodic physical measures (metric entropy and Lyapunov spectra), and (III) macroscopic ensemble statistics (variance and transport flux). In the forced two-well Duffing oscillator, high-resolution numerical analyses reveal the origin of classical predictive failures: dense homoclinic tangles degenerate into non-retaining transient saddles (h_T > 0, h_KS = 0) collapsing to periodic sinks, whereas macroscopic chaos persists past primary homoclinic tangency via higher-order saddle relays. Generalizing to periodic-potential rotational systems shows that heteroclinic crossings and resonant Shapiro steps enforce geometric bounds on phase slips and transport. Structurally disentangling informational capacity from energetic realization connects geometric mechanics with non-equilibrium statistical observability, offering a new diagnostic framework for noise-induced instabilities in nonlinear systems.
ER -