v8.1-3D: Three-Dimensional Scan of Intrinsic Transition Measures in a Phenomenological Two-Mode Jaynes-Cummings Model — Technical Note
Year: 2026
Type: preprint
Abstract: This technical note documents the three-dimensional extension (v8.1-3D) of the intrinsic transition measures previously introduced in Track A v8.1. It is a **phenomenological and methodological** contribution: it uses the two-mode Jaynes-Cummings formalism with Lindblad dissipation as an effective language for two coexisting dynamical modes, and it does not claim that the underlying system is quantum. ## What is formal and verifiable The model is a two-mode Jaynes-Cummings system with Lindblad dissipation, integrated with BDF. The threshold-free measures of the coexistence product $P(t) = R(t) \cdot I(t)$ — $A_{\text{coex}}$, $P_{\text{max}}$, $t_{\text{peak}}$, $W_{1/2}$, $\tau_{\text{eff}}$, $\eta$, and the `peak_reached` flag — are mathematically well defined and reproducible from the released code and CSV files. ## What is phenomenological The Jaynes-Cummings formalism is used here as an effective description, not as a claim about the microscopic nature of the system. The two modes and their coupling are phenomenological ingredients. The Lindblad dissipator models loss of coherence and population relaxation in a generic way. This is a standard use of the formalism outside its original quantum-optical domain, analogous to effective models in computational neuroscience or complex-systems physics. ## What is informative / reproducible A $6 \times 6 \times 6$ scan over $(g, \gamma_\phi, \gamma_a)$ with $N_0 = 12$, $t_{\text{max}} = 50$, $n_{\text{steps}} = 600$, joblib parallelism with 2 jobs, total runtime $\approx 4$ h 1 min. All numeric values in the PDF have been cross-verified against the released CSV and report files. ## What is explicitly out of scope Any interpretation of the intrinsic measures as proxies for consciousness states, endogenous/exogenous access, or neural dynamics is **not claimed** in this note. The model does not assert that the brain is a quantum system. The purpose of this release is methodological: to document a reproducible numerical procedure and its threshold-free measures. ## Main findings 1. The trade-off statement of v8.1 is corrected: in the full 3D space, $A_{\text{coex}}$ and $\tau_{\text{eff}}$ are positively correlated ($r = +0.54$), and the real trade-off is between $P_{\text{max}}$ and $\tau_{\text{eff}}$ ($r = -0.18$ to $-0.28$). 2. $92.1\%$ of bio cells reached their peak; the remaining 17 cells are reported as **lower bounds**, not final values. 3. Absolute values of v8.1 and v8.1-3D are **not directly comparable** because $N_0$ and $n_{\text{steps}}$ differ. The qualitative trends agree; the absolute numbers do not. 4. The results are robust across two grid resolutions ($5 \times 5 \times 5$ vs $6 \times 6 \times 6$). ## Contents of this release This release includes two complementary PDF documents: - **Technical note** (8 pages): documents the v8.1-3D run, the numerical scheme, the analysis pipeline, the main results, and the correction to the trade-off statement of v8.1. - **Field equations** (11 pages): a didactic and progressive exposition of all field equations used in the model, with physical motivation and mathematical justification for each equation. In addition, the release includes the full $6 \times 6 \times 6$ CSV scan, the checkpoint file, pivot tables per $\gamma_a$ slice, the generating Python script with four switchable presets, and the automatic analysis report. This update supersedes the earlier intermediate versions (v7, v7.1, v7.3) and is intended as a companion to the v8.1 data release. ## Relationship to v8.1 The v8.1-3D extension is a strict superset of v8.1 in the parameter space. It confirms all qualitative trends of v8.1, extends the analysis to a third axis ($\gamma_a$), and corrects one interpretive statement about the trade-off between coexistence and duration. Nothing in v8.1 is invalidated. The DOI of v8.1 remains unchanged.
Author: Miguel Percudani
Language: English
Topic: Complex Systems and Dynamics
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
OpenAlex ID: W7214537180
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