PhysicsLogic / Callen-Welton 1951

Thermal Inference and Relative Calibration

Common gain uncertainty cancels; independent detector and drive uncertainty can conceal a different state.

Definitions and assumptions

Scope and physical limitations

This four-level diagnostic retains the same nondegenerate Hamiltonian, positive normalized stationary states, and all three separately resolved adjacent probes. Detector A = g Q and drive B = h Q are actual Hermitian operators; the perturbation is +V(t) B. Noise scales as g squared and response as g h. When h = g is nonzero, three exact noise/response ratios plus normalization and commutation identify Gibbs at beta = 1 without knowing the absolute gains. With uncertain relative gains, an explicit different population and strictly positive couplings instead reproduce all Gibbs records for every time. Every channel has nonzero noise and response. These are exact coordinate correlations, not finite-sample inference, general tomography, or Callen-Welton's force-noise spectrum. The alternative is excluded at the declared temperature, not at every possible temperature.

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Examples and distinctions

Constructed examples of this model; each answer includes the Lean statement.

Exact root statement

¬access.RecordConstrainsValueAt () (records reference) fun state => state = density ensemble.density
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