What if you could cool a mechanical resonator to the quantum regime without an optical cavity? Resolved-sideband cooling has been the workhorse of quantum optomechanics for two decades, but it demands high-finesse optical cavities (Q > 10⁵) — a requirement that categorically excludes some of the most promising mechanical platforms: graphene membranes, carbon nanotubes, transition metal dichalcogenides, and CMOS-integrated devices. These "optically dark" resonators possess exceptional mechanical properties yet remain locked out of active quantum cooling. This paper introduces ETEC (Entropic Transfer via Entanglement Collapse), a theoretical protocol that bypasses this limitation entirely. Rather than exchanging photons with a cold cavity, ETEC treats cooling as an information-processing task: mechanical excitations are coherently mapped onto the electronic spin of a nitrogen-vacancy (NV) center in diamond via intense magnetic field gradients (∇B ≈ 10⁵–10⁶ T/m), temporarily shelved in nuclear spin memory, and erased through optical pumping — exporting entropy to the photon bath at the thermodynamic cost dictated by Landauer's principle. The key innovation is nuclear spin shelving, which suppresses residual heating during optical reset by 4–5 orders of magnitude, enabling sustained operation over >10⁵ cycles. Numerical simulations based on the Lindblad master equation project steady-state phonon occupations of ⟨n⟩ ≈ 0.4–10 depending on experimental parameters. Sensitivity analysis reveals that ETEC is heating-limited, not coupling-limited — a finding that directly informs experimental design priorities. ETEC does not compete with sideband cooling; it extends active quantum control into the complementary regime where no such pathway previously existed. This is a condensed 14-page paper suitable for journal submission. The comprehensive manuscript (120 pages, spanish) containing full derivations, extended numerical simulations, and detailed appendices is available at: https://doi.org/10.5281/zenodo.18443971 Explicit falsification criteria and a three-year experimental roadmap are provided.
Arturo Ramos Ruiz (Thu,) studied this question.