Beyond Redfield: Thermodynamic Bounds and Non-Perturbative Quantum Dynamics in Tubulin Networks

Quantum effects in biology are unavoidable at the molecular scale; the unresolved question is whether they can remain functionally relevant across the timescale gap between femtosecond molecular dynamics and microsecond-to-millisecond biological function. Here we formalize this mismatch as an equilibrium-to-functionality gap and use tubulin as a stringent open-system test case.

We combine secular Lindblad, Redfield, and hierarchical equations of motion (HEOM) treatments to quantify decoherence, non-perturbative relaxation, and the physical amplification required for functional relevance. Equilibrium dephasing yields a conservative fs at 310 K, with a generic protein-bath baseline of ≈ 13 fs. A completed 30 ps HEOM trajectory for the full 1JFF tryptophan network shows distributed non-Markovian relaxation, with terminal purity Pur = 0.210 and stretched-exponential exponent β _KWW ≈ 0.44, confirming that Redfield is useful as a short-time perturbative comparator but not quantitatively interchangeable with HEOM in this intermediate-coupling regime.

We introduce a coherence-utility criterion 𝒰 = 𝒦 τ _coh /τ _func , separating required amplification from empirically bounded gain. A thermodynamic uncertainty relation closure shows that neural-scale cascade amplification would require P _min ∼ 10 ⁻⁷ W, about five orders of magnitude above the local microtubule GTP budget. Fröhlich pumping is found to be linewidth-gated rather than generically micron-scale; ordered-water cavity QED and geometric subradiance remain experimentally testable but severely constrained candidates.

The result is not a model of consciousness, but a reproducible physical benchmark framework for evaluating biological quantum-coherence claims under explicit open-system, energetic, and experimental constraints. Six falsifiable experimental programmes are prioritized, and the full computational framework is released with a validation ledger, cryptographic audit trail, and living supplementary material.

Abstract Figure

Graphical abstract.

Equilibrium tubulin coherence lies in the femtosecond regime, while functional neural timescales lie in the millisecond regime. Fröhlich pumping, QED-cavity protection, and geometric subradiance remain experimentally discriminable non-equilibrium candidates requiring independently bounded amplification.

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Versioned computational scope of this release

This manuscript reports the theoretical framework, calibrated equilibrium baseline, Redfield/HEOM validation ledger, stratified Bayesian evidence synthesis, classical comparators, and falsifiable experimental design. The release-specific reproduction audit, including the current validation-check total and the SHA-256 fingerprints of the binary production artefacts ( .npz , .pkl ), is documented in LIVING_SI.md and outputs_data/raw_json/structur al/validation_report.json . A completed 30 ps HEOM production trajectory has been validated on constrained hardware; the master dataset contains the full 8-site population trajectory. A summary of those results is provided in § 2.2.5 . All claims made below are restricted to the numerical and theoretical evidence reported in this manuscript and its associated repository artefacts. The public repository ships the calibrated phenomenological baseline for accessibility; the HEOM production artefacts serve as the non-perturbative validation benchmark. All source figure outputs associated with this release are maintained in the public repository under outputs_data/figures_final/ .