Exergy, Critical Entropy, and the Fate of Complex Systems: A Physical-Statistical Framework for Predicting Socioeconomic Trajectories

This paper addresses the "growth without development" problem in emerging economies by proposing a novel physical-statistical framework to diagnose structural barriers. It introduces the concept of Systemic Exergy (B) as a measure of an economy's effective capacity to convert available resources into inclusive growth. Furthermore, it presents the notion of Critical Entropy (S _crit ) as the tipping point where labor informality ceases to be adaptive and becomes a structural impediment. Applied to Mexico from 2005–2023, the model quantifies how the system transitioned into stagnation in 2015. The results reveal that current growth stimuli (e.g., nearshoring) are largely dissipated due to systemic inefficiencies. The model emphasizes that long-term development requires reducing informality below the critical threshold, rather than relying solely on GDP growth. Economies are conceptualized as complex systems far from equilibrium, where internal disorder can surpass a critical threshold, preventing energy from translating into useful socioeconomic transformation. The model's formulation for the Fate of the System (D) is D = B - T(S - S _crit ) , where T is Temperature (normalized annual GDP growth) and S is Social Entropy (normalized labor informality rate). This equation demonstrates that when entropy exceeds the critical threshold, the dissipative term grows, preventing systemic transformation. Policy implications suggest increasing B (addressing inequality), reducing S (implementing inclusion policies), and directing T (ensuring investment drives productive transformation). JEL Codes: O11, O47, C63, D63, P48