Abstract: This mathematical essay brings together ideas from Economics, Geobiodynamics and Thermodynamics. Its purpose is to obtain real models of complex evolutionary systems. More specifically, the essay defines Roegenian Economy and links Geobiodynamics and Roegenian Economy. In this context, we discuss the isomorphism between the concepts and techniques of Thermodynamics and Economics. Then we describe a Roegenian economic system like a Carnot group. After we analyse the phase equilibrium for two heterogeneous economic systems. The European Union Economics appears like Cartesian product of Roegenian economic systems and its Balance is analysed in details. A Section at the end describes the "economic black holes" as small parts of a a global economic system in which national income is so great that it causes others poor enrichment. These ideas can be used to improve our knowledge and understanding of the nature of development and evolution of thermodynamic-economic systems.
The paper introduces a formal Thermodynamic-Economic Dictionary that establishes an isomorphism between state variables across economics and thermodynamics.
It models Roegenian economic systems as both commutative and non-commutative Carnot groups, detailing concepts like phase equilibrium and the economic mole.
The study extends its framework to the EU economy and defines economic black holes, offering a novel paradigm for anticipating macroeconomic shifts.
Geobiodynamics and Roegenian Economic Systems
This essay presents a sophisticated mathematical exploration that merges concepts from Economics, Geobiodynamics, and Thermodynamics to model the complex behaviors of evolutionary systems. It seeks to establish an isomorphic relationship between thermodynamic and economic systems by defining the Roegenian Economy, inspired by Nicholas Georgescu-Roegen's pioneering work in linking entropy with economic processes.
Thermodynamics-Economic Isomorphism
The paper introduces a Thermodynamic-Economic Dictionary that draws parallels between state variables in both domains, showcasing a formal analytical analogy. It reflects a belief that thermodynamic principles can extend to economic systems, offering a fresh perspective on the systemic interactions and dynamics within macroeconomics. The thermodynamics-economics correspondence is crucial for understanding phenomena such as 'economic black holes', characterized by extensive national income resulting in surrounding poverty.
Roegenian Economic Systems and Phase Equilibrium
The Roegenian economic system is mathematically modeled as both a commutative and non-commutative Carnot group, providing an algebraic structure that parallels thermodynamic systems. The paper further explores the phase equilibrium of heterogeneous economic systems, introducing the concept of 'economic mole' as a measure of value in commodities and money phases within an isolated economic system.
European Union Economics Balance
The paper extends its theoretical framework to the European Union's economic system, conceptualized as a Cartesian product of Roegenian economic systems. It theorizes equilibrium states governed by the interaction of 27 independent economic subsystems, each characterized by specific distributions and subject to nonholonomic constraints. Achieving steady-state equilibrium is deemed utopian, with adjusted balance through weighted averages offering a practical approach.
Economic 3D Black Holes
A provocative extension of astrophysical black hole models is applied to economics, defining economic black holes using parameters analogous to thermodynamic state variables: entropy, national income, total investment, and economic spin. The paper speculates on inequalities such as Y>I, Y≥J​, inviting exploration into their descriptive implications.
Implications and Future Directions
The paper posits that the Roegenian economy reveals laws akin to thermodynamic principles, potentially explaining macroeconomic phenomena such as collapse and turmoil. By prioritizing the Thermodynamic-Economic Dictionary's complex equivalence and Pfaff equations as nonholonomic constraints, the paper suggests a new paradigm for economic analysis that integrates interdisciplinary methodologies. It underscores the need for advanced simulations and geometric analyses to further investigate the novel concepts elucidated.
Conclusion
The essay underscores the potential of thermodynamic models in economic contexts, reinforcing the notion that Roegenian economic systems inherently harbor principles analogous to those of thermodynamics. It challenges contemporary economists to engage with mathematical methodologies to anticipate and mitigate economic ruptures, advocating for a shift towards nonlinearity and complexity in economic thought and education.