A Global Relaxation Principle for Cosmic Acceleration: Quantum-Thermodynamic Motivation and Relativistic Consistency Tests

This work proposes and tests a model–independent global relaxation principle for the late–time cosmological background, motivated by horizon thermodynamics and quantum coarse–graining. The principle states that the deceleration parameter obeys an averaged consistency bound, ⟨q(zmax) − q(zt)⟩ ≤ 0, where zt denotes the transition to acceleration and zmax the maximum redshift effectively supported by observations. The bound is statistical and allows local fluctuations and nonmonotonic behavior while constraining the net coarse–grained evolution. A quantum–thermodynamic motivation is formulated as the Quantum–Thermodynamic Relaxation Hypothesis (QTRH), in which the apparent horizon is treated as an open quantum system whose macroscopic observables satisfy relaxation inequalities rather than deterministic trajectories. The prediction is tested using likelihood–weighted, nonparametric reconstructions of H(z) from cosmic chronometers, Type Ia supernovae, and baryon acoustic oscillations, with analytic marginalization over standard nuisance parameters. The reconstructed integrated estimator strongly supports the relaxative branch in the configurations adopted here. Finally, the previously introduced relativistic closure tests (LERAC) are interpreted as the classical, observational projection of the same relaxation principle onto independent matter and light sectors. The unified framework is sharply falsifiable: a statistically significant violation of the averaged bound would rule out both QTRH and its classical realization.