Admissibility and Stability in Thermodynamic Systems: A Tier-7 Instantiation within the Paton System

Thermodynamics describes macroscopic system behaviour through conservation laws and entropy constraints that determine which state transitions are physically permitted. This paper presents a structural interpretation of thermodynamic stability within the Paton System, a domain-neutral framework for analysing admissibility and continuation in constrained systems. Thermodynamic evolution is interpreted as recursive state transitions constrained by energy conservation and entropy conditions. Continuation occurs only when state updates remain within the admissible region defined by these constraints. Thermodynamic equilibrium corresponds to a stable admissibility basin, while irreversible processes correspond to directional evolution constrained by entropy. This work demonstrates that thermodynamic laws can be understood as constraint structures governing admissible continuation, providing a Tier-7 physical domain instantiation of the structural principles of the Paton System.