# Economic Cycles of Carnot Type

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## 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

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

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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