ZFCρ Thermodynamics Paper V: The Channel-Normalized Winding Ratio — Dynamical Prediction of the Tsallis q Parameter in State-Coupled Oscillators / ZFCρ热力学论文 V:通道归一化卷绕比与Tsallis q的动力学预测

Thermo IV established the exact interpolation family q = 1 + 1/K and listed independently extracting K from dynamics as its hardest testable prediction. This paper realizes that prediction for the first time on the Brusselator chemical oscillator.

The central finding: in a continuous-time oscillator, K is not the one-lag effective depth m_eff(τ) — which diverges as 1/τ — but the channel-normalized winding ratio K_dyn = T/(n_ch · τ_dec), where T is the oscillation period, τ_dec is the radial decay time, and n_ch = 2 is the forward/reset channel count. The Tsallis q is predicted as q = 1 + n_ch · τ_dec / T, a zero-free-parameter formula requiring only two macroscopic timescales from the autocorrelation function. Across b = 2.2–5.0 (seven points), MAE = 0.022 with maximum |Δq| = 0.068, outperforming fixed-τ methods which collapse at extreme parameters.

Two negative results sharpen Thermo IV's open problem 2: (1) m_eff(τ) ∝ 1/τ is a representation effect; (2) the inverse participation ratio K_part = 1/Σw² fails because ACF mode weights are not microscopic shielding-layer weights at finite βE.

Part of the ZFCρ / Self-as-an-End (SAE) research program.

Keywords

Tsallis statistics; q-exponential; non-equilibrium thermodynamics; chemical oscillator; Brusselator; autocorrelation function; winding ratio; channel-averaged shielding; nonextensive statistical mechanics; SAE; ZFCρ

Related Identifiers

• IsPartOf: ZFCρ Thermodynamics Series
• References: 10.5281/zenodo.19605664 (Thermo IV)
• References: 10.5281/zenodo.19597684 (Thermo III)
• References: 10.5281/zenodo.19511064 (Thermo II)
• References: 10.5281/zenodo.19310282 (Thermo I)

License

Creative Commons Attribution 4.0 International (CC BY 4.0)

Version

v1.0

Language

English (with Chinese companion version)

Subjects

• Statistical mechanics
• Nonlinear dynamics
• Chemical kinetics
• Mathematical physics

Notes

Fifth paper in the ZFCρ Thermodynamics sub-series. Companion Chinese version: sae-thermo-V-cn-draft-v2.md Project website: https://self-as-an-end.net