Nonequilibrium Calibration and Faithful Records in Autonomous Effective Measurement Models

Can an autonomous quantum apparatus produce approximately Born-distributed outcomes and faithfully preserve its own earlier measurement label without assuming complete initial quantum equilibrium?

This paper presents two finite autonomous Schrödinger–Bohmian constructions with explicit error bounds under restricted nonequilibrium initial laws. Each construction addresses three separate requirements: outcome calibration, copying the actual earlier configuration label, and retaining that label throughout a specified holding interval.

The first model combines periodic focusing, a finite recoiling reference rotor, and a delayed compensated oscillator. Its record-distribution error is at most 0.004434840087, while failure to copy and retain its actual earlier label is at most 0.002327254798.

The second model begins with a small radial Gaussian, includes autonomous preparation and activation, and incorporates the record writer from the original entrance. The joint law of its earlier label and complete symbolic holding record differs from an ideal constant Born-labelled record by less than 0.006086770113 in total variation. Its actual-label copy-and-hold failure probability is below 0.000552421956.

The proofs combine bounded-variation calibration, exact recoil reduction, conditional-rank current estimates, finite-clock derivative bounds, and absolute probability-current estimates over the entire holding interval. The specialized derivations and coefficient calculations are included in the manuscript’s appendices.

The two models retain distinct Hamiltonians and statistical assumptions. Neither establishes universal relaxation from arbitrary initial laws, supplies physical sources for every prescribed interaction, or demonstrates laboratory realization. External specialist verification remains open.