Abstract
This paper introduces the Hamiltonian Higher-Order Elasticity Dynamics (2HOED) framework, a novel, domain-agnostic methodology that integrates principles of classical mechanics into the analysis of complex systems. By extending the Hamiltonian formalism to include higher-order elasticity terms (position, velocity, acceleration, and jerk), 2HOED provides a dynamic, energy-based diagnostic tool for understanding systemic behavior across disciplines such as economics, climate science, epidemiology, and supply chain logistics. The framework transforms time-varying elasticities into interpretable energy metrics like System Power, Inertia, and Marginal Response, enabling early detection of tipping points, resilience thresholds, and feedback loops. Unlike traditional econometric models or machine learning approaches, 2HOED is computationally lightweight, transparent, and requires minimal data, making it accessible for real-time diagnostics. The paper demonstrates the utility of 2HOED through an application to the Kuznets environmental theory, analyzing the relationship between CO2 emissions and GDP growth. The framework bridges gaps between econometrics, machine learning, and causal inference, offering a unified approach to dynamic diagnostics and policy design.
Methodology
The 2HOED framework begins by estimating a time-varying elasticity (e.g., CO2 vs GDP) as a 'position' variable. Successive derivatives (velocity, acceleration, jerk) are computed empirically, and these are embedded into a Hamiltonian energy function. This yields interpretable metrics such as System Power, Marginal Response, and Sensitivity to shocks. The approach relies on rolling regressions and simple mathematical operations, avoiding the need for large datasets or complex machine learning models. The framework is illustrated using the Kuznets environmental theory to analyze GDP-CO2 dynamics.
Results
The application of 2HOED to the Kuznets environmental theory revealed dynamic insights into the relationship between CO2 emissions and GDP growth. Peaks in System Power indicated stored systemic stress, while jerk spikes highlighted impending regime shifts. The framework successfully identified leverage points for policy intervention and provided a transparent, real-time diagnostic map of the system's energy dynamics.
Implications
2HOED has broad implications across disciplines, offering a scalable and interpretable tool for dynamic diagnostics. It can be used to anticipate crises, design adaptive policies, and engineer robust systems in fields such as economics, climate science, epidemiology, and supply chain management. By bridging gaps between econometrics, machine learning, and causal inference, the framework enables decision-makers to better understand and influence complex systems in real time.
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