# The entropy of nations: Global energy inequality lessens, but for how long?

##### Jan 03, 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.)

Studies of world energy consumption often feature plots of energy consumption or population over time. Yakovenko and his colleagues prefer to draw out the underlying exponential distribution of national energy use by plotting the fraction of world population versus per-capita consumption.

The JQI researchers draw on data from the U.S. Energy Information Administration (EIA). It covers the period from 1980 to 2010 and includes numbers from more than 200 countries; see figure 1. Their results are published in the Journal "Entropy" (2). A few years ago Yakovenko made a similar study of national per-capita income distributions (3).

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 2 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.

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 2, 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 2 represents this middle case, where, in the competition for scarce energy resources, neither total equality nor total inequality reigns.

Of course, the labels along the curves are a stark reminder that some nations get much more than the average and some nations much less. In Figure 2 the slope of the curve at any one point corresponds to the per-capita energy consumption. So the upper right of each curve is inhabited by the high-consuming nations: USA, Russia, France, UK. And the lower-left, lower-slope positions on the curve include Brazil and India. The movement of China upwards on the curve is the most dramatic change over the past 40 years.

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, showing 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 that of the JQI curve. However, he was charting the decline of global income inequality by tracking the a parameter called purchasing power parity (PPP) among nations (4).

Can it continue?

The JQI curve suggests that the trend toward lesser inequality in energy consumption will start stalling out, as the energy consumption distribution begins to approach full exponential behavior. Is this because of the inexorable applicability of the laws of thermodynamics to national ? Just as with gas molecules, where some molecules are "rich" (possess high energy) and others "poor," are some nations destined to be rich and others poor?

Maybe not. Professor Yakovenko believes that one obvious way to alter the circumstances of energy distribution expressed in the figures above is the further development of renewable sources of energy. "These graphs apply to a well-mixed, globalized world, where a finite pool of fossil fuels is redistributable on a global scale. If the world switches to locally-produced and locally-consumed renewable energy and stops reshuffling the deck of cards (fossil fuels), then the laws of probability would not apply, and can be lowered further. After all, the Sun shines roughly equally on everybody."

Yakovenko adds that for an exponential distribution what he calls "the rule of thirds" will be in effect. This means the top 1/3 of the world population will consume 2/3 of the total produced energy while the bottom 2/3 of the population will consume only 1/3 of the total energy.

Explore further: It's a negative on negative absolute temperatures

More information: "Global Inequality in Energy Consumption from 1980 to 2010," Scott Lawrence, Qin Liu, and Victor M. Yakovenko, published online at Entropy, 16 December 2013 www.mdpi.com/1099-4300/15/12/5565

## Related Stories

#### Inequality and investment bubbles

Apr 19, 2012

"Money, it's a gas," says the sixties rock group Pink Floyd in their song "Money." Indeed, physics professor Victor Yakovenko is an expert in statistical physics and studies how the flow of money and the distribution ...

#### Half of greenhouse gases 'emitted by five nations'

Dec 01, 2011

More than half of all carbon pollution released into the atmosphere comes from five countries, according to a national ranking of greenhouse gas emissions released Thursday.

#### It's a negative on negative absolute temperatures

Dec 20, 2013

The concept of a perpetual motion machine is an enticing one: Imagine a machine that runs continuously without requiring any external energy—a feat that could make refueling vehicles a thing of the past.

#### CO2 emissions +2.2% in 2012, driven by China and coal

Nov 19, 2013

Emissions of carbon dioxide from fossil fuels and cement production reached a new high in 2012, rising 2.2 percent over 2011 due chiefly to an increase in coal-burning China, scientists said Tuesday.

#### World set to heat up despite clean-energy efforts, IEA warns

Nov 12, 2013

Global warming is set to heat up with temperatures rising to nearly twice targets set by the United Nations, the International Energy Agency warned on Tuesday.

#### World population not likely to stabilize at 10 billion people

Mar 20, 2013

Projections suggesting the world human population will stop growing around 10 billion people at the end of this century are improbable, according to new research by SFI Postdoctoral Fellow Marcus Hamilton and collaborators.

## Recommended for you

#### Switch on sunlight for a brighter future

2 hours ago

Imagine sitting in a windowless room yet having the feeling of the sun shining on your face. This unique experience is now possible thanks to the COELUX EU-funded project which recreates the physical and ...

#### The shocking link between politics and electricity in India

3 hours ago

(Phys.org) —About a third of India's electricity is lost each year. It just never gets billed. Some is stolen or disappears because of technical problems. It's enough power to light up all of Italy for ...

#### US urged to drop India WTO case on solar

17 hours ago

Environmentalists Wednesday urged the United States to drop plans to haul India to the WTO to open its solar market, saying the action would hurt the fight against climate change.

#### Is nuclear power the only way to avoid geoengineering?

Apr 23, 2014

"I think one can argue that if we were to follow a strong nuclear energy pathway—as well as doing everything else that we can—then we can solve the climate problem without doing geoengineering." So says Tom Wigley, one ...

#### Finalists named in Bloomberg European city contest

Apr 23, 2014

Amsterdam wants to create an online game to get unemployed young people engaged in finding jobs across Europe. Schaerbeek, Belgium, envisions using geothermal mapping to give households personalized rundowns of steps to save ...

#### Bloomberg invests \$5M in solar-powered lamp

Apr 22, 2014

Former New York Mayor Michael Bloomberg's foundation has announced a \$5 million investment in an artsy-looking solar-powered lamp designed for use in off-grid populations in Africa.

##### Returners
3 / 5 (2) Jan 03, 2014
The distribution of energies among molecules in a gas and the distribution of per-capita energy consumption among nations both obey an exponential law.

This is Rather intuitive due to the concept of "Cultural Exchange". Additionally, the U.S. and European governments and corporations actually promote this distribution, for reasons that aren't exactly clear to me, though an explanation of what I mean can't fit in 1000 characters nor perhaps 10,000.

This means the top 1/3 of the world population will consume 2/3 of the total produced energy while the bottom 2/3 of the population will consume only 1/3 of the total energy.

This is close to known natural mathematical law.

However, inequality within nations is far greater than this, and is roughly 90/10 relationship, which is far more biased than natural law predicts should happen. Thus indicating statistically significant corruption and bias in the economic system, almost entirely favoring the top.

## More news stories

#### Researcher develops method for monitoring whether private information is sufficiently protected

Tri Minh Ngo, researcher at the University of Twente, has developed a new method for monitoring whether private information is sufficiently protected in computer programs. His technology can be used to check ...

#### Computer algorithm outperforms humans on 'Labeled Faces in the Wild' benchmark

(Phys.org) —For the first time a computer has beaten the human average when attempting to discriminate between faces in the Labeled Faces in the Wild (LFW) dataset. The team from China that programmed the ...

#### FCC to propose pay-for-priority Internet standards (Update)

The Federal Communications Commission is set to propose new open Internet rules that would allow content companies to pay for faster delivery over the so-called "last mile" connection to people's homes, but enhance scrutiny ...

#### Review: 'Hearthstone' card game is the real deal

Video game publishers don't take many risks with their most popular franchises. You know exactly what you are going to get from a new "Call of Duty" or "Madden NFL" game—it will probably be pretty good, ...

#### SensaBubble: It's a bubble, but not as we know it (w/ video)

Multi-sensory technology that creates soap bubbles, which can have images projected onto them or when the bubbles are burst release a scent, will be unveiled at an international conference later this month.

#### Your T-shirt's ringing: Telecommunications in the spaser age

(Phys.org) —A new version of "spaser" technology being investigated could mean that mobile phones become so small, efficient, and flexible they could be printed on clothing.

#### Cheetahs found to use spatial avoidance techniques to allow for surviving among lions

(Phys.org) —A team of researchers at the University of Minnesota, along with assistance from several African wildlife agencies, has found that contrary to popular belief, cheetahs are able to maintain population ...

#### How a plant beckons the bacteria that will do it harm

A common plant puts out a welcome mat to bacteria seeking to invade, and scientists have discovered the mat's molecular mix.

#### Research splits alligator snapping turtle, 'dinosaur of the turtle world,' into three species

The alligator snapping turtle is the largest river turtle in North America, weighing in at up to 200 pounds and living almost a century. Now researchers from Florida and the University of Vermont have discovered ...

#### Tiny magnetic DNA particles protect olive oil from counterfeiters

Who guarantees that expensive olive oil isn't counterfeit or adulterated? An invisible label, developed by ETH Zurich researchers, could perform this task. The tag consists of tiny magnetic DNA particles ...