| Massimiliano Ferrara†
Abstract: 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). Keywords: Roegenian economics, econophysics, phase diagrams, Gibbs-Pfaff equation, thermodynamic-economic correspondence, triple point. MSC: 91B02, 91B55, 80A10, 37N40. DOI 10.56082/annalsarscimath.2026.2.161 †massimiliano.ferrara@unirc.it, Universit`a degli Studi Mediterranea di Reggio Calabria, Dipartimento DiGiES, Decisions LAB; ICRIOS- Bocconi University, Milan, Italy |
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application,
ISSN ONLINE 2066 – 6594
|
