Abstract
The subject of this paper is to analyse the Mathematical Principia of Economic 3D Black Holes in Roegenian economics. In detail, we study two main problems: (i) mathematical origin of economic 3D black holes; and (ii) entropy and internal political stability depending on national income and the total investment, for economic Reissner–Nordström (RN) 3D black hole. To solve these problems, it was necessary to jump from macroeconomic side to microeconomic side (a substantial approach as they are so different), to complete the thermodynamics–economics dictionary with new entities, and to introduce the flow between two macroeconomic systems. The main contribution is about introducing and studying the Schwarzschild-type metric on an economic 4D system, together with Rindler coordinates, Einstein 4D partial differential equations (PDEs), and economic RN 3D black holes. In addition, we introduce some economic Ricci type flows or waves, for further research.
Highlights
The primary purpose of this article is to show that all economics principles, obtained via thermodynamics, are not in conflict but can be integrated seamlessly to complement each other. the results arise by combining and developing rapidly and successfully the previous notions, they do not depend on modeling/analysis tradeoffs
Our main contribution is a compositional mathematical language for Roegenian economics that combines thermodynamics, differential geometry and economics, along with a proof calculus and expressibility results. It is the basic objective of this paper to give answers to the following questions: What does a thermodynamics–economics morphism look like? What differential laws do we have in Roegenian economics? Do the gravitational models in physics have a correspondent in economics? What are the black holes in economics and are they
What are the economic relationships between pair and pair? Does economic entropy have the basic properties of a general entropy? Can we estimate the entropy of the United States, China Entropy, etc.? Can economic flows and economic waves be characterised as partial differential equations (PDEs) solutions? After a long period of gradual progress, Roegenian economics is handled by Pfaff equations and PDE systems that produce the geometric equivalents
Summary
The primary purpose of this article is to show that all economics principles, obtained via thermodynamics, are not in conflict but can be integrated seamlessly to complement each other. Our main contribution is a compositional mathematical language for Roegenian economics that combines thermodynamics, differential geometry and economics, along with a proof calculus and expressibility results. It is the basic objective of this paper to give answers to the following questions: What does a thermodynamics–economics morphism look like? Beyond the establishment of entropy of an economic black hole, the various sections of this paper implement in numerous ways the general theory borrowed from thermodynamics, physics and differential geometry. Our main result is contained in Theorem 3, Section 4: An economic black hole is characterised by entropy and internal political stability, depending explicitly on the (national) income and the total investment. His research has contributed significantly to the development of bio-economy and eco-economy
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