# Global Inequality in Energy Consumption from 1980 to 2010

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## Abstract

**:**

## 1. Introduction

**Figure 1.**Historical trends (1980–2010) and future projections (2020–2040) for total and per-capita energy consumption (red and blue circles), as well as ${\mathrm{CO}}_{2}$ emissions (red and blue crosses), along with ${\mathrm{CO}}_{2}$ intensity (green circles) and human population (black curve).

**Figure 2.**Stack plots of energy consumption (

**left panel**) and population (

**right panel**) the in USA, China, India and the rest of the world from 1980–2010 based on the data from EIA, Energy Information Administration.

## 2. Theoretical Analogy with Statistical Physics

## 3. Energy Consumption Distribution

#### 3.1. Cumulative Probability Distribution Function

**Figure 3.**(

**Left panel**) Complementary cumulative probability distribution function, Equation (1), of the global energy consumption per capita in 2010 (red curve), compared with an exponential fit (black dashed curve). The inset shows the same plot in log-linear scale. (

**Right panel**) Lorenz plots for the global energy consumption per capita in 1980–2010 (colored curves), compared with an exponential distribution (black solid curve).

#### 3.2. Lorenz Curves

**Figure 4.**(

**Left panel**) Parametric plots of the empirical ${y}_{\mathrm{emp}}\left(x\right)$ vs. exponential ${y}_{\mathrm{exp}}\left(x\right)$ cumulative fractions of global energy consumption using the population fraction, x, as a parameter. (

**Right panel**) Parametric plots of the empirical ${x}_{\mathrm{emp}}\left(y\right)$ vs. exponential ${x}_{\mathrm{exp}}\left(y\right)$ cumulative population fractions using the energy consumption fraction, y, as a parameter.

#### 3.3. Gini Coefficient

**Figure 5.**Historical evolution of the global Gini coefficient, G (circles), for energy consumption per capita (

**left panel**) and ${\mathrm{CO}}_{2}$ emissions per capita (

**right panel**). The blue dashed line represents a linear extrapolation and the red dashed-dotted curve a sigmoid fit. The horizontal line at $G=0.5$ corresponds to an exponential distribution.

#### 3.4. The Law of 1/3

**the top 1/3 of the world population consumes 2/3 of energy**, which we call

**the law of 1/3**. This simple and easily understandable statement summarizes the current state of global inequality in energy consumption. We are not aware of this result to have been known before. Because it is a consequence of the principle of maximal entropy, we expect that the global energy consumption inequality will stay at this level in the future.

## 4. ${\mathbf{CO}}_{\mathbf{2}}$ Emissions Distribution

**Figure 6.**(

**Left panel**) Complementary cumulative probability distribution function of the global ${\mathrm{CO}}_{2}$ emissions per capita in 2010 (red curve), compared with an exponential fit (black dashed curve). The inset shows the same plot in log-linear scale. (

**Right panel**) Lorenz plots for the global ${\mathrm{CO}}_{2}$ emissions per capita in 1980–2010 (colored curves), compared with an exponential distribution (black solid curve).

**Figure 7.**(

**Left panel**) Parametric plots of the empirical ${y}_{\mathrm{emp}}\left(x\right)$ vs. exponential ${y}_{\mathrm{exp}}\left(x\right)$ cumulative fractions of global ${\mathrm{CO}}_{2}$ emissions using the population fraction, x, as a parameter. (

**Right panel**) Parametric plots of the empirical ${x}_{\mathrm{emp}}\left(y\right)$ vs. exponential ${x}_{\mathrm{exp}}\left(y\right)$ cumulative population fractions using the ${\mathrm{CO}}_{2}$ emissions fraction, y, as a parameter.

**Figure 8.**Historical evolution of the global Gini coefficients for natural gas, coal and petroleum consumption per capita.

## 5. Discussion and Conclusions

## Supplementary Materials

Supplementary File 1Supplementary File 2## Acknowledgments

## Conflicts of Interest

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**MDPI and ACS Style**

Lawrence, S.; Liu, Q.; Yakovenko, V.M.
Global Inequality in Energy Consumption from 1980 to 2010. *Entropy* **2013**, *15*, 5565-5579.
https://doi.org/10.3390/e15125565

**AMA Style**

Lawrence S, Liu Q, Yakovenko VM.
Global Inequality in Energy Consumption from 1980 to 2010. *Entropy*. 2013; 15(12):5565-5579.
https://doi.org/10.3390/e15125565

**Chicago/Turabian Style**

Lawrence, Scott, Qin Liu, and Victor M. Yakovenko.
2013. "Global Inequality in Energy Consumption from 1980 to 2010" *Entropy* 15, no. 12: 5565-5579.
https://doi.org/10.3390/e15125565