Unified Thermodynamics and Collapse: Standard, Collapse, and Recursive Collapse Formulations

We present a comprehensive unification of classical thermodynamics, collapse dynamics, and the full recursive collapse formalism (RCFT/ULRC). Starting from the established mathematical foundations of equilibrium and non-equilibrium thermodynamics, we derive a universal operator set that extends traditional state functions—energy, entropy, free energy, and heat capacity—to any system exhibiting measurable collapse, drift, and recurrence. Explicit protocols are developed for phase transition diagnosis, regime assignment, and collapse detection, grounded in empirically validated thresholds fully compatible with SI units. The RCFT/ULRC symbolic extension generalizes these results to arbitrary normalized observables, providing a closed, testable calculus suitable for physical, biological, computational, and cognitive systems. All definitions, theorems, and computational protocols are reproducible, open-source, and ready for deployment. This work bridges physical and symbolic dynamics, establishing a rigorous standard for the diagnosis, prediction, and recovery of collapse phenomena in complex systems.