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The Entropy of Nations
Global energy inequality lessens, but for how long?
January 2, 2014

The 18th century writer Adam Smith provided a workable metaphor for the way society utilizes resources. In his book “The Wealth of Nations,” he argued that even as individuals strive, through personal industry, to maximize their advantage in life, they inadvertently contribute---as if under the influence of a “hidden hand”---to an aggregate disposition of wealth. Well, if Smith were a physicist and alive in the 21st century he might be tempted to compare people or nations to molecules and to replace the phrase “hidden hand” with “thermodynamic process.”

EXPONENTIAL BEHAVIOR

Victor Yakovenko, a scientist at the Joint Quantum Institute (1), studies the parallels between nations and molecules. The distribution of energies among molecules in a gas and the distribution of per-capita energy consumption among nations both obey an exponential law. That is, the likelihood of having a certain energy value is proportional to e^(-E/kT), where T is the temperature and k is a proportionality factor called Boltzmann’s constant. (“Temperature” here is taken to be the average national per-capita energy consumption in the world.)

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Actually, the consumption data can be graphed in another way, one that illustrates the distributive nature of energy use. In a “Lorenz plot,” both the vertical and horizontal axes are dimensionless. Figure 3 shows data curves for four years---1980, 1990, 2000, and 2010. The progression of curves is toward a fifth curve which stands for the idealized exponential behavior.

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MAXIMUM ENTROPY

This fifth curve corresponds to a state of maximum entropy in the distribution of energy. Entropy is not merely a synonym for disorder. Rather, entropy is a measure of the number of different ways a system can exist. If, for example, $100 was to be divided among ten people, total equality would dictate that each person received $10. In Figure 3, this is represented by the solid diagonal line. Maximum inequality would be equivalent to giving all $100 to one person. This would be represented by a curve that hugged the horizontal axis and then proceeded straight up the rightmost vertical axis.

Statistically, both of these scenarios are rather unlikely since they correspond to unique situations. The bulk of possible divisions of $100 would look more like this example: person 1 gets $27, person 2 gets $15, and so forth down to person 10, who receives only $3. The black curve in Figure 3 represents this middle case, where, in the competition for scarce energy resources, neither total equality nor total inequality reigns.

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INEQUALITY

The inequality between the haves and have-nots is often characterized by a factor called the Gini coefficient, or G (named for Italian sociologist Corrado Gini), defined as area between the Lorenz curve and the solid diagonal line divided by half the area beneath the diagonal line. G is then somewhere between 0 and 1, where 0 corresponds to perfect equality and 1 to perfect inequality. The curve corresponding to the maximum-entropy condition, has a G value of 0.5.

The JQI scientists calculated and graphed G over time. Figure 4 shows how G has dropped over the years. In other words, inequality in energy consumption among the nations has been falling. Many economists attribute this development as a result of increased globalization in trade. And as if to underscore the underlying thermodynamic nature of the flow of commodities, a recent study by Branko Milanovic of the World Bank features a Gini curve very similar to Figure 4. However, he was charting the decline of global income inequality by tracking the a parameter called purchasing power parity (PPP) among nations (4).

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