Entropy of Reissner–Nordström 3D Black Hole in Roegenian Economics

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.

Economic Cycles of Carnot Type

“…In the following, we reproduce again the correspondence between the characteristic state variables and the laws of thermodynamics with the macro-economics ingredients as described in Udriste et al (2002Udriste et al ( -2019) based on the theory on which the economics was founded in 1971 [6]. They also allow us to include in the economics the idea of a "black hole" with a similar meaning to the one in astrophysics [5].…”

“…The formal analytical-mathematical analogy between economics and thermodynamics is accepted by economists and physicists as well (what differs are the dictionaries used). Starting from these remarks, the papers of Udriste and coauthors [1][2][3][4][5] build a morphism of dictionary type between thermodynamics and economics, admitting that fundamental laws in thermodynamics are transferred into laws for economics.…”

“…(ii) In this paper it is only a morphism based on an initial dictionary conceived by Udriste's research team. Different parts of this dictionary (morphism) can be found in the papers [1,5] and references therein. A full discussion of the thermodynamics-economics morphism will be produced in a future paper.…”

“…The thermodynamics-economics dictionary (morphism) allows the transfer of information from one discipline to its image (Udriste et al [1,5]), keeping the background of the first discipline that we think was suggested by Roegen in 1971 [6].…”

“…Let (G, I, E, P, Q) be economic variables, according the previous dictionary (G = growth potential, I = internal politics stability, E = entropy, P = price level (inflation), Q = volume, structure, quality). We refer again the Roegenian economics (an economic distribution) generated by the Gibbs-Pfaff fundamental equation dG − IdE + PdQ = 0 on R 5 .…”