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title, date, draft, tags
| title | date | draft | tags | |||
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| Research Paper: Biophysical Witness Dynamics: Quantum Darwinism in Microtubule Conformational States (Letter) | 2026-06-01T08:00:00Z | false |
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Abstract: We apply the principles of Quantum Darwinism to the conformational dipole states of tubulin dimers within cellular microtubules. By defining a pure dephasing interaction with an Ohmic aqueous thermal bath, we formally parameterize the decoherence rate \gamma. We calculate the Mutual Information I(S; E_F) across multiple independent acoustic phonon fragments. By demonstrating that the Holevo bound is saturated, we compute the explicit redundancy factor R_\delta, proving that stable, classical tubulin pointer states are robustly imprinted into the biological environment.
Microtubule Dephasing and the Ohmic Bath
Let a single tubulin dimer be modeled as a two-level open quantum system representing its conformational dipole, H_S = \frac{\omega_0}{2} \sigma_S^z. The environment consists of acoustic phonon modes in the intra-cellular fluid. We define a pure dephasing interaction H_{int} = \sum_k g_k (\sigma_S^z \otimes \sigma_{E_k}^z).
The bath is characterized by an Ohmic spectral density:
J(\omega) = \sum_k |g_k|^2 \delta(\omega - \omega_k) = \alpha \omega e^{-\omega/\omega_c}
where \alpha is the dimensionless coupling strength derived from molecular dipole-water interactions, and \omega_c is the high-frequency cutoff of the solvation shell. At biological temperatures T=310 K (k_B T \gg \omega_c), the Markovian decoherence rate is explicitly parameterized as \gamma \approx \frac{2\pi \alpha}{\hbar} k_B T.
Redundant Imprinting and the Holevo Bound
We partition the cellular environment into disjoint fragments E_F. The mutual information I(S; E_F) scales with the fragment size f. For pure dephasing, the environment perfectly records the pointer states (the diagonal elements of \rho_S). The Holevo bound I \approx H(S) is saturated for small fractions f.
The redundancy factor R_\delta, defined as the number of independent environmental fragments that supply the missing information 1-\delta, is explicitly given by:
R_\delta = \frac{1}{f_\delta} \approx \frac{\gamma}{\gamma_{frag} \ln(1/\delta)}
Given the massive degrees of freedom in the biological solvation shell, R_\delta \gg 1, proving that numerous independent biochemical pathways can concurrently deduce the classical conformational state of the tubulin dimer without perturbing its Hamiltonian.
References
- [Zurek2009] W. H. Zurek, Nat. Phys. 5, 181 (2009).
- [Plenio2008] M. B. Plenio, S. F. Huelga, New J. Phys. 10, 113019 (2008).