Traditional International Relations theories, due to the vagueness of core concepts and <br> the static nature of their explanatory frameworks, have consistently encountered <br> bottlenecks in revealing the nonlinear dynamic mechanisms behind the evolution, <br> mutation, and collapse of state systems. Based on non-equilibrium thermodynamics <br> and topological dynamics, this paper proposes a novel theoretical paradigm termed <br> the "Structural Evolution School," redefining the state system as an <br> energy-information composite dissipative structure. <br> The core innovation of this research lies in achieving a threefold breakthrough: 1) The <br> mathematical reconstruction of theoretical concepts – quantifying abstract notions like <br> power structure and ideology into the "Physical Topology Index (Φₚ)" and the "Mental <br> Topology Index (Φₘ)," thereby defining the key state variable "Cognitive Entropy Locking (Θ)"; 2) The parametric modeling of human irrationality – transforming <br> behavioral traits such as greed, hatred, and delusion into computable "Internal <br> Systemic Resistance (Ω)" and its sub-dimensions for the first time; 3) The <br> endogenous dynamic upgrade of the model – by constructing bidirectional feedback <br> differential equations among parameters (e.g., the vicious cycle between the defensive <br> realist perturbation factor δ and cognitive entropy locking Θ), fundamentally <br> resolving the inherent flaw of traditional models where parameters are exogenous and <br> lack evolutionary dynamics. <br> Through the revised Dissipative Structure Stability Equation and Monte Carlo <br> simulations, the study finds that the survival boundary of a state system is not <br> determined by total potential energy but depends on the dynamic race between <br> effective energy conversion efficiency and the rate of entropy increase. Among the <br> numerous parameters, the Cognitive Entropy Locking Coefficient (Θ) and the <br> Religious Coupling Coefficient (λᵣ) constitute the key order parameters governing the <br> system's phase transitions (stability, transformation, or collapse). Historical case <br> retrospection and modern state validation demonstrate the model's exceptional <br> robustness in explaining the rise and fall of civilizations. Ultimately, this research constructs a complete pathway from theoretical diagnosis to policy intervention, <br> providing a new mathematical foundation for understanding and shaping the <br> evolutionary resilience of complex systems.