# Economic Cycles of Carnot Type

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

## 1. Thermodynamic-Economic Dictionary

**Remark**

**1.**

THERMODYNAMICS | ECONOMICS | |

U = internal energy | … | G = growth potential |

T = temperature | … | I = internal politics stability |

S = entropy | … | E = entropy |

P = pressure | … | P = price level (inflation) |

V = volume | … | Q = volume, structure, quality |

M = total energy (mass) | … | Y = national income (income) |

Q = electric charge | … | $\mathcal{I}$ = total investment |

J = angular momentum | … | J = economical investment angular momentum |

(spin) | (investment spin) | |

M = M(S,Q,J) | … | Y = Y(E,$\mathcal{I}$,J) |

$\mathsf{\Omega}=\frac{\partial M}{\partial J}$ = angular speed | … | $\frac{\partial Y}{\partial J}$ = marginal inclination to investment turnover |

$\mathsf{\Phi}=\frac{\partial M}{\partial Q}$ = electric potential | … | $\frac{\partial Y}{\partial \mathcal{I}}$ = marginal inclination to investment |

${T}_{H}=\frac{\partial M}{\partial S}$ =Hawking temperature | … | $\frac{\partial Y}{\partial E}$ = marginal inclination to entropy |

${\mu}_{k}$ = chemical potentials | … | ${\nu}_{k}$ = economical potentials |

**Remark**

**2.**

**Definition**

**1.**

## 2. What Is the Carnot Cycle in Thermodynamics?

**Remark**

**3.**

## 3. Economic Carnot Cycle, $\mathbf{Q}-\mathbf{P}$ Diagram

**Remark**

**4.**

## 4. Economic Carnot Cycle, $\mathbf{E}-\mathbf{I}$ Diagram

**Theorem**

**1.**

**Proof.**

## 5. Efficiency of an Economic System

**Definition**

**2.**

## 6. Economic Carnot Cycle—Problems and Solutions

**1**. If financial assets market (production of goods) absorbed by the engine is ${q}_{1}$ = 10,000 c.u. (conventional units), what is the wealthy of the system done by the economic Carnot engine?

**Known**: The absolute internal politics stability of the consumption ${I}_{C}=400\%$, the absolute internal politics stability of the production ${I}_{H}=800\%$, the financial assets market (production of goods) input ${q}_{1}$ = 10,000 c.u.

**Wanted**. Wealthy of the system done by economic Carnot engine W.

**Solution**. The efficiency of the economic Carnot engine $e=\frac{{I}_{H}-{I}_{C}}{{I}_{H}}$, $e=\frac{1}{2}$.

**2**The absolute internal politics stability of the production is ${I}_{H}=600\%$ and the absolute internal politics stability of the consumption is ${I}_{C}=400\%$. If the wealthy done by engine is W, what is the financial assets market output?

**Known**: The absolute internal politics stability of the consumption ${I}_{C}=400\%$, the absolute internal politics stability of the production ${I}_{H}=600\%$.

**Wanted**. Financial assets market output ${q}_{2}$.

**Solution**. The efficiency of economic Carnot engine is $e=\frac{{I}_{H}-{I}_{C}}{{I}_{H}}$, $e=\frac{1}{3}$. The wealthy of the system done by economic Carnot engine is $W=e{q}_{1}$, $3W={q}_{1}$. It follows the stock market: ${q}_{2}={q}_{1}-W=2W$.

**3**An economic Carnot engine has an efficiency of $0.3$. Its efficiency is to be increased to $0.5$. By what must the internal politics stability of the source be increased if the sink is at $300\%$?

**Solution**Efficiency is given by $e=1-\frac{{I}_{2}}{{I}_{1}}$. Here $e=0.3$. From $0.3=1-\frac{300}{{I}_{1}}$, it follows ${I}_{1}=428.6\%$. For increased efficiency of $0.5$, the source internal politics stability should be $0.5=1-\frac{300}{{I}_{1}}$, i.e., ${I}_{1}=600\%$. Hence the source internal politics stability should be increased by $600-428.6=171.4$ (%).

## 7. Ideal Income Case

## 8. Economic Van der Waals Equation

**Remark**

**5.**

**Remark**

**6.**

**Theorem**

**2.**

## 9. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Acknowledgments

## Conflicts of Interest

## References

- Udriste, C.; Ferrara, M.; Opris, D. Economic Geometric Dynamics; Monographs and Textbooks 6; Geometry Balkan Press: Bucharest, Romania, 2004. [Google Scholar]
- Udriste, C.; Ferrara, M. Multitime models of optimal growth. WSEAS Trans. Math.
**2008**, 7, 1, 51–55. [Google Scholar] - Udriste, C.; Ferrara, M.; Zugravescu, D.; Munteanu, F. Nonholonomic geometry of economic systems. In Proceedings of the 4th European Computing Conference, ECC’10, Wisconsin, United States, 20–22 April 2010; Grigoriu, M., Mladenov, V., Bulucea, C.A., Martin, O., Mastorakis, N., Eds.; World Scientific and Engineering Academy and Society (WSEAS): Stevens Point, WI, USA, 2010; pp. 170–177. [Google Scholar]
- Udriste, C. Optimal control on nonholonomic black holes. J. Comput. Methods Sci. Eng.
**2013**, 13, 271–278. [Google Scholar] [CrossRef] - Udriste, C.; Ferrara, M.; Zugravescu, D.; Munteanu, F. Entropy of Reisner-Nordström 3D black hole in Roegenian economics. Entropy
**2019**, 21, 509. [Google Scholar] [CrossRef] [PubMed][Green Version] - Georgescu–Roegen, N. The Entropy Law and Economic Process; Harvard University Press: Cambridge, MA, USA, 1971. [Google Scholar]
- Jakimowicz, A. The role of entropy in the development of economics. Entropy
**2020**, 22, 452. [Google Scholar] [CrossRef] [PubMed] - Mimkes, J. A Thermodynamic Formulation of Economics. Chapter in Econophysics and Sociophysics: Trends and Perspectives; Bikas, K., Chakraborti, A., Chatterjee, A., Eds.; WILEY-VCH Verlag GmbH & Co. KGaA: Weinheim, Germany, 2006; pp. 1–33. [Google Scholar]
- Mimkes, J. Concepts of Thermodynamics in Economic Growth. In The Complex Networks of Economic Interactions; Namatame, A., Kaizouji, T., Aruka, Y., Eds.; Lecture Notes in Economics and Mathematical Systems; Springer: Berlin/Heidelberg, Germany, 2006; Volume 567. [Google Scholar] [CrossRef]
- Chernavski, D.S.; Starkov, N.I.; Shcherbakov, A.V. On some problems of physical economics. Phys. Usp.
**2002**, 45, 9, 977–997. [Google Scholar] [CrossRef] - Ruth, M. Insights from thermodynamics for the analysis of economic processes. In Non-Equilibrium Thermodynamics and the Production of Entropy: Life, Earth, and Beyond; Kleidon, A., Lorenz, R., Eds.; Springer: Heidelberg, Germany, 2005; pp. 243–254. [Google Scholar]
- Udriste, C.; Ferrara, M.; Zugravescu, D.; Munteanu, F. Controllability of a nonholonomic macroeconomic system. J. Optim. Theory Appl.
**2012**, 154, 3, 1036–1054. [Google Scholar] [CrossRef] - Bianciardia, C.; Donatib, A.; Ulgiatic, S. On the relationship between the economic process, the Carnot cycle and the entropy law. Ecol. Econ.
**1993**, 8, 1, 7–10. [Google Scholar] [CrossRef] - Creţu, T.I. Physics; Technical Editorial House: Bucharest, Romania, 1996. (In Romanian) [Google Scholar]
- Ouerdane, H.; Apertet, Y.; Goupil, C.; Lecoeur, P. Continuity and boundary conditions in thermodynamics: From Carnot’s efficiency to efficiencies at maximum power. Eur. Phys. J. Spec. Top.
**2015**, 224, 839–864. [Google Scholar] [CrossRef][Green Version] - Udriste, C.; Golubyatnikov, V.; Tevy, I. Economic cycles of Carnot type. arXiv
**2018**, arXiv:1812.07960v1. [Google Scholar] - Udriste, C.; Ferrara, M.; Tevy, I.; Zugravescu, D.; Munteanu, F. Phase Diagram for Roegenian Economics. Atti della Accademia Peloritana dei Pericolanti Classe di Scienze Fisiche, Matematiche e Naturali
**2019**, 97, 1, A3. [Google Scholar] [CrossRef] - van der Waals, J.D. The equation of state for gases and liquids. In Nobel Lectures, Physics 1901–1921; Elsevier Publishing Company: Amsterdam, The Netherlands, 1967; pp. 254–265. [Google Scholar]
- Isard, W. Location theory and trade theory: Short-run analysis. Q. J. Econ.
**1954**, 68, 2, 305. [Google Scholar] [CrossRef] - Khrennikov, A. Thermodynamic-like Approach to Complexity of the Financial Market (in the Light of the Present Financial Crises). In Decision Theory and Choices: A Complexity Approach; Faggini, M., Vinci, C.P., Eds.; Springer: Berlin/Heidelberg, Germany, 2010; pp. 183–203. [Google Scholar]
- Khrennikov, A. The financial heat machine: Coupling with the present financial crises. Wilmott
**2012**, 57, 32–45. [Google Scholar] [CrossRef]

**Figure 2.**Economic Carnot cycle acting as an economic process with an engine producing goods, illustrated on a E-I diagram.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Udriste, C.; Golubyatnikov, V.; Tevy, I.
Economic Cycles of Carnot Type. *Entropy* **2021**, *23*, 1344.
https://doi.org/10.3390/e23101344

**AMA Style**

Udriste C, Golubyatnikov V, Tevy I.
Economic Cycles of Carnot Type. *Entropy*. 2021; 23(10):1344.
https://doi.org/10.3390/e23101344

**Chicago/Turabian Style**

Udriste, Constantin, Vladimir Golubyatnikov, and Ionel Tevy.
2021. "Economic Cycles of Carnot Type" *Entropy* 23, no. 10: 1344.
https://doi.org/10.3390/e23101344