Soft Model Selection and Structured Assembly of Observables for Micro–Macro Transitions, Operational Relativity, and Emergent Thermodynamics

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Abstract

An operational meta-model is presented for transitions among quantum, classical, relativis- tic, and thermodynamic descriptions without forcing a single master state space. Unification is performed at the level of observable predictions: each formalism produces an output in a common space Y defined by a feature map Φ (moments, spectra, correlations, or other functionals). Convex weights are assigned via a standard soft selection rule (softmax / Gibbs form) from losses, with entropic regularization and a complexity penalty (AIC/BIC/MDL) to reduce bias toward overly expressive models. Physics-facing priors are encoded through calibrated dimensionless knobs for decoherence/classicality, relativistic severity, and ther- modynamicity, yielding a regime-aware gating layer. A simple out-of-catalog diagnostic (surprise/residual monitoring) is included to flag persistent mismatch that may indicate missing observables or missing models. A minimal case study template (harmonic oscillator with a bath) and an acid test in the NISQ regime (critical decoherence) are outlined as reproducible validation pathways.

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