# The Impact of Entropy Production and Emission Mitigation on Economic Growth

## Abstract

**:**

## 1. Introduction: The Second Law of Thermodynamics and Economics

## 2. Entropy Production and Emissions

#### 2.1. Balances

#### 2.2. Dissipation

**r**of this system is

#### 2.3. Pollution Functions

- (a)
- Integrating Equation (5) over the volume V of the system, and dividing it by V yields the system’s average entropy-production density at time t as ${\overline{\mathsf{\sigma}}}_{S}\left(t\right)={\sum}_{i=0}^{N}{p}_{i}$, where ${p}_{0}\equiv \frac{1}{V}{\int}_{V}{\mathbf{j}}_{Q}\nabla \frac{1}{T}\mathrm{d}V$ is defined as thermal pollution, and ${p}_{i>0}\equiv \frac{1}{V}{\int}_{V}{\mathbf{j}}_{i}[-\nabla ({\mathsf{\mu}}_{i}/T)+{\mathbf{f}}_{i}/T]\mathrm{d}V$ is defined as pollution by the particles of sort $i=k=1\cdots N$.
- (b)
- We assume that for each type i of pollution there is a critical limit ${p}_{Ci}$ defined by society—often in a long process starting with growing awareness of damages from pollution and ending in legal emission limits. Until the middle of the 20th century, in the highly industrialized countries, high chimneys had been one of the principal technologies to reduce damages from emissions in the neighborhood of the emitting source. However, nowadays, it is no longer tolerated that air currrents spread the dirt from a source country to its neighbors, forcing them to become a polluted sink, or to the global biosphere. Therefore, ${p}_{Ci}$ is not only defined by the society that produces the emissions, but in the case of transboundary pollutants by the international community as well. A prominent example is the United Nations’ 2015 Paris agreement to reduce CO${}_{2}$ emissions, with different mitigation obligations for different countries.
- (c)
- The approach to the critical limit ${p}_{Ci}$ is mitigated by solar exergy input into the biosphere and thermal radiation into space. Their biological and physical pollution-abating effects are summarized by the natural purification rate ${p}_{0i}$. As long as pollution ${p}_{i}$ is so small that ${p}_{i}<<{p}_{0i}<<{p}_{Ci}$, society is not worried by it and does not fight it directly. This was the case for CO${}_{2}$ emissions until the 1980s and is still true for heat emissions.

## 3. Economic Growth and Pollution

#### 3.1. Growth of Total Output

#### 3.2. Growth of Conventional Output

#### 3.2.1. “Polluted” Growth Equation

#### 3.2.2. Thermoeconomic Energy and Cost Optimization

#### 3.2.3. Nuclear Exit, CO${}_{2}$ Abatement, and Photovoltaics Implementation

## 4. Summary and Outlook

## Acknowledgments

## Conflicts of Interest

## References and Notes

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**Figure 1.**Optimized potentials of energy conservation by heat-exanger networks, heat pumps, and cogeneration in the Federal Republic of Germany as a function of the price $b\left(F\right)$ of one unit of fuel F [37]. $N\left(F\right)$ is the annual quantity of primary energy required to satisfy the fixed demand for process heat and electricity. C and ${C}_{0}$ are the total annual costs of providing $N\left(F\right)$ with and without energy-saving technologies. Solid $N\left(F\right)$ curve: upper cost limit is $1.0{C}_{0}$; dashed curve: upper limit is $1.1{C}_{0}$. Note the suppressed zero point of the $N\left(F\right)$ ordinate. The figure is reproduced with kind permission of H.-M. Groscurth.

**Figure 2.**Growth of installed PV capacity (lower curve, left ordinate, GW) and of annual PV refunding (upper curve, right ordinate, billion Euros) in Germany. This figure is reproduced with kind permission of H. Wirth. It is part of a forthcoming English version of [51]. Solid curves: actual data, dashed curves: projections.

Energy System | Specific Total Life–cycle CO${}_{2}$ Emissions, g/kWh |
---|---|

Lignite-fired power plant | 850–1200 |

Hard-coal-fired power plant | 700–1000 |

Natural-gas-fired power plant | 400–550 |

Photovoltaic cell | 70–150 |

Gas-powered combined heat and power unit | ≈ 50 |

Water power plant | 10–40 |

Nuclear power plant | 10–30 |

Wind park | 10–20 |

**Table 2.**Primary energy consumption in Germany [49].

Year | 1991 | 1992 | 1999 | 2000 | 2010 | 2011 | 2012 | 2013 | 2014 |
---|---|---|---|---|---|---|---|---|---|

${10}^{15}$ J | 14,750 | 14,400 | 14,350 | 14,401 | 14,044 | 13,750 | 13,380 | 13,723 | 13,077 |

**Table 3.**Shares of energy carriers in German primary energy consumption, in percent, rounded. Source: Arbeitsgemeinschaft Energiebilanzen.

Year | Mineral Oil | Natural Gas | Coal | Lignite | Nuclear Energy | Renewables |
---|---|---|---|---|---|---|

2010 | 33 | 22 | 12 | 11 | 11 | 9 |

2011 | 33 | 21 | 13 | 12 | 9 | 11 |

2013 | 33 | 22 | 13 | 12 | 8 | 11 |

2014 | 35 | 21 | 13 | 12 | 8 | 11 |

**Table 4.**Shares of renewable energies in German electricity generation, in percent, rounded. Sources: Arbeitsgemeinschaft Energiebilanzen and Bundesverband der Energie- und Wasserwirtschaft.

Year | Total | Wind | Biomass | Water | Photovoltaics | Domestic Waste |
---|---|---|---|---|---|---|

2011 | 20 | 8 | 5 | 3 | 3 | 1 |

2013 | 23 | 8 | 7 | 3 | 5 | n.a |

**Table 5.**Specific emissions of CO${}_{2}$ from German electricity generation, ${I}_{1}$, and consumption ${I}_{2}$ [50]. For the indicators ${I}_{1}$ and ${I}_{2}$ see the text.

Year | 1991 | 2000 | 2007 | 2010 | 2011 | 2012 | 2013 |
---|---|---|---|---|---|---|---|

${I}_{1}$, g/kWh | 744 | 627 | 602 | 542 | 558 | 562 | 559 |

${I}_{2}$, g/kWh | 745 | 623 | 623 | 559 | 564 | 586 | 595 |

**Table 6.**German gross domestic product (GDP) until 2014 and GDP${}_{a}$ afterwards, and refunding ${\Lambda}_{PV}$ of PV-electricity generation according to scenarios A and B, in billion Euros. ${\Lambda}_{PV}$-numbers of scenario A are from Figure 2 and the linear average of the upper curve after 2013, ${\Lambda}_{PV}$-numbers of scenario B are constructed by adding 2 billion Euros per year to the 2011 refunding in Figure 2. GDP is from Table 7, GDP${}_{a}$ is from Equation (35).

Year | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 |
---|---|---|---|---|---|---|---|---|

GDP||GDP${}_{a}$ | 2670 | 2691 | 2698 | 2740 | 2765 | 2790 | 2815 | 2840 |

${\Lambda}_{PV}$,scenario A | 8 | 9 | 9.5 | 9.7 | 9.9 | 10.1 | 10.3 | 10.5 |

${\Lambda}_{PV}$, scenario B | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 |

**Table 7.**German gross domestic product (GDP) after German reunification, inflation-corrected, chained, in billion Euros${}_{2010}$, rounded; and growth rates. Source: Statistisches Bundesamt [55].

Year | 1991 | 1992 | 1999 | 2000 | 2010 | 2011 | 2012 | 2013 | 2014 |
---|---|---|---|---|---|---|---|---|---|

GDP, ${10}^{9}$ Euros | 2045 | 2076 | 2286 | 2358 | 2580 | 2670 | 2691 | 2698 | 2740 |

growth rate, % | n.a | 1.5 | 1.9 | 3.2 | 3.9 | 3.7 | 0.6 | 0.4 | 1.6 |

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**MDPI and ACS Style**

Kümmel, R.
The Impact of Entropy Production and Emission Mitigation on Economic Growth. *Entropy* **2016**, *18*, 75.
https://doi.org/10.3390/e18030075

**AMA Style**

Kümmel R.
The Impact of Entropy Production and Emission Mitigation on Economic Growth. *Entropy*. 2016; 18(3):75.
https://doi.org/10.3390/e18030075

**Chicago/Turabian Style**

Kümmel, Reiner.
2016. "The Impact of Entropy Production and Emission Mitigation on Economic Growth" *Entropy* 18, no. 3: 75.
https://doi.org/10.3390/e18030075