ADVANCES ON PHASE DIAGRAMS FOR ROEGENIAN ECONOMICS: THEORY AND EMPIRICAL VALIDATION

This paper extends the foundational work on Roegenian Economics by developing a rigorous mathematical framework for the thermodynamic-economic correspondence initiated by Georgescu-Roegen. We provide an enhanced dictionary between thermodynamic and economic state variables. The main contributions include: (i) a formal proof of the existence and uniqueness of the economic triple point; (ii) characterization theorems for critical phenomena; (iii) derivation of Maxwell type relations for economic potentials; and (iv) stability analysis via Legendre transforms. We present empirical validation using World Bank Governance Indicators and IMF inflation data for 2022-2023, demonstrating that the phase diagram captures the relationship between institutional stability and price dynamics. The analysis identifies candidates for triple point behavior (Venezuela, Zimbabwe) and supercritical regimes (Switzerland, Singapore).