A Quantitative Criterion for the Quantum–Classical Transition: Open-System Dynamics and Residual Coherence Bounds in Inflation

Description: This work presents a quantitative framework for describing the quantum–classical transition as a continuous dynamical process governed by open quantum system interactions. A normalized Quantum Persistence Function is introduced to measure residual quantum coherence, allowing classical emergence to be characterized through a scale-dependent suppression criterion. The model is constructed using a microscopic spin–boson open-system foundation and extends decoherence analysis to inflationary cosmology. The framework connects dynamical decoherence bounds with observational constraints derived from primordial statistics measured by the Planck Collaboration. The formulation builds conceptually on decoherence theory associated with Wojciech H. Zurek and provides a diagnostic criterion for residual coherence survival across cosmological scales. The results aim to provide a practical quantitative tool for evaluating classicalization efficiency in inflationary models and for relating open-system quantum dynamics to empirical cosmological observations. KEYWORDS: Quantum–classical transition; decoherence theory; open quantum systems; inflationary cosmology; residual quantum coherence; spin–boson model; classicalization dynamics; primordial perturbations; cosmological quantum mechanics