Model D Quantum Bridge: A Two-State Rotor-Oscillator Hybrid with Thermal, Work-Store and Autonomous Energy-Depot Controls

This theoretical preprint develops a limited bridge from a specified two-state Hamiltonian with coherent coupling paths to a phase-dependent small-displacement stiffness. Reciprocal Ehrenfest forces and torque yield a conservative energy account; classical Langevin bath couplings and work-store or autonomous energy-depot controls extend the comparison to heat and supplied work. The autonomous free-depot branches have analytically determined rates that depend on the parameters. No independent selection of 0.218 Hz is obtained. A sustained mean rate and a shared phase are distinct, and the stochastic ensembles are independent repeats of one rotor, not a coupled rotor network. Illustrative scaled inputs are used throughout; physical Hz labels are conditional on a chosen reference time. The Born rule is an input. Material realization, global hybrid stability, full quantum Gibbs equilibrium and a complete Model-D embedding remain open. The package supplies the manuscript, source, figures, numerical records and integrity checks. No new empirical measurements or live Model-D integration are reported.