Observation as Selection Pressure: Operational Definition of the Field ρψ and Its Thermodynamic Reduction

Preprint. Publicly released on Zenodo prior to journal submission. This preprint gives an operational definition of an observation-induced “selection pressure” field ρψ(x,t) that unifies directed measurement back-action and isotropic thermal agitation within a single, experimentally calibratable structure. Observation is modeled as a point process of small SU(2) kicks U ≈ exp(−i(δθ/2)n·σ) with arrival rate νψ and an axis–angle distribution P(n,δθ|x,t). From these statistics, the field is defined as a triplet ρψ ≡ {S0, πψ, Qψ}, where S0 sets the isotropic update strength, πψ encodes vectorial directedness, and Qψ captures anisotropy. For a two-level system with gap ℏω, the framework yields transition rates Γ↑ = S0(1−v) and Γ↓ = S0(1+v), with v = (πψ·ẑ)/S0. Imposing detailed balance leads to a one-to-one temperature map v = tanh(ℏω/2kBTeff), so Teff is determined solely by v, while S0 controls relaxation speed (τeq = 1/(2S0)) and transport scale. The tensor Qψ governs how noise power partitions between energy relaxation and dephasing, enabling a reduction of T1 and T2 into components of ρψ. A minimal three-step calibration protocol is proposed to reconstruct S0, v (and Teff), and Qψ from standard measurements (Γ↑, Γ↓, T1, T2) across platforms such as continuously monitored superconducting qubits, collective spin ensembles, and back-action–sensitive nanomechanical resonators. The preprint also states falsifiable predictions and discusses how a minimal phase step ε provides a microscopic route to the unattainability of absolute zero.