Lorenz curves for global inequality in energy consumption and CO_{2} emissions were constructed in the paper by

S. Lawrence, Q. Liu, and V. M. Yakovenko,

"Global inequality in energy consumption from 1980 to 2010",

Entropy **15**, 5565 (2013),
PDF,
arXiv:1312.6443

The paper was also covered in a JQI press release "The Entropy of Nations" by Phillip Schewe.

Raw data are from the U.S. Energy Information Administration (EIA). Source code is available at arxiv.org/format/1312.6443, and movie files at arxiv.org/src/1312.6443v2/anc. The two videos below show computer animation of evolution in time of the Lorenz curves from 1980 to 2010.

Lorenz curves for global inequality in energy consumption and in CO_{2} emissions per capita:

In both graphs, small circles indication various countries, whereas big circles indicate some labeled countries. We observe that the Lorenz curves for energy consumption and CO_{2} emissions look quite similar. This is not surprising, given that most energy comes from fossil fuels anyway, although there are some differences for individual countries (e.g. for France because of nuclear energy).

The Lorenz curves for 1980 exhibit a sharp slope change in the middle, separating two groups of countries. One group in the top-right has high slope, indicating high energy consumption and CO_{2} emissions per capita. This group consists of "developed" countries, mostly in North America and Europe. Another group in the bottom-left has low slope, indicating low energy consumption and CO_{2} emissions per capita. This group consists of "developing" countries, such as China, India, and Brazil.

In the subsequent years since 1980, we observe that the Lorenz curves move up, meaning that **global inequality decreases**. By 2010, the cusp in the middle of the Lorenz curves has smoothed out. Now there is no sharp boundary between "developed" and "developing" countries anymore. This is largely due to China moving to the middle of the curve between "developed" and "developing" countries.

The black curve represents the (analytically) calculated Lorenz graph for an exponential distribution. In statistical physics, the latter corresponds to the Boltzmann-Gibbs distribution, which maximizes entropy in thermal equilibrium. We observe that the empirical Lorenz curves move toward the calculated black exponential curve, approaching it from below. The paper interpreted this behavior as evolution of the global economy toward the state of maximal entropy, accelerated by the globalization process.

The Lorenz curves for 2010 are already quite close to the exponential curve, indicating that the state of maximal entropy has been almost reached. Thus the paper predicted that further decrease in global inequality **will stop** soon, and the Lorenz curves will not significantly change anymore. These predictions have been confirmed in the follow-up paper described below, when the data for subsequent years became available.

The data up to 2017 were analyzed in the paper by

Gregor Semieniuk and Victor M. Yakovenko

"Historical evolution of global inequality in carbon emissions and footprints versus redistributive scenarios"

Journal of Cleaner Production **264**, 121420 (2020),
PDF,
arXiv:2004.00111

It was difficult to perform data analysis for energy consumption for technical reasons, so only the data for CO_{2} emissions are shown here. The two graphs below show the Lorenz curves and the Gini coefficient up to 2017.

The Lorenz curves for 1980-2010 are the same as discussed above. But there is virtually **no difference** between the new Lorenz curve for 2017 (red) and the earlier one for 2010 (blue). This is in agreement with the prediction of the first paper that evolution stops once the Lorenz curve reaches an exponential distribution (black).

The Gini coefficient *G* for 1980-2010 (black circles) from the first paper shows a decreasing trend and no sign of saturation yet. In contrast, the new data points for 2011-2017 (red squares) exhibit saturation at the level of *G*=0.5. The (analytically) calculated value of the Gini coefficient for an exponential distribution is *G*=0.5, and saturation at this level was predicted in the first paper.

In conclusion, the new data up to 2017 show that global inequality in CO_{2} emissions **stopped decreasing** soon after 2010. This observation has profound consequences for strategies and scenarios dealing with climate change. Importantly, the saturation of global inequality at the level *G*=0.5 **confirms the prediction** made in the first paper on the basis of the maximal entropy principle. Remarkably, this prediction was made at the time when global inequality has been steadily decreasing, and there was no indication of saturation in the available data yet. The advanced prediction and the subsequent confirmation lend strong support to the proposition that economic globalization is governed by the principle of maximal entropy.

For more information on the subject, see https://physics.umd.edu/~yakovenk/econophysics/.

*Last update
2023-6-19*

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