Growth-Entropy-Geometry: A Constraint-Based Framework for Cosmology and Regime Transitions

This preprint presents a constraint-based framework in which physical and dynamical evolution is indexed by accumulated irreversible growth rather than by coordinate time. Growth is defined as the formation of persistent structure and is fundamentally constrained by entropy production, while sustained growth requires sufficient entropy export capacity. The framework is formalized using explicit growth–entropy equations and illustrated through toy simulations that demonstrate phase transitions between growth-dominated and entropy-capacity–dominated regimes. These ideas are applied to early-universe cosmology (including inflation, horizons, the arrow of time, and late-time accelerated expansion) as well as to nonlinear atmospheric forecasting, where the framework functions as a shadow-mode diagnostic for regime transitions such as rapid intensification. This work does not modify established physical equations or operational forecast models. Instead, it provides an interpretive and diagnostic layer consistent with general relativity and standard numerical forecasting systems, with potential applications in understanding predictability, regime shifts, and forecast confidence in complex dynamical systems.