Saturday, December 26, 2009

Post # 4: Energy, Entropy, and the GDP

Much is made about the fact the U.S., with only 4.5% of the world’s population (~ 308M), accounts for 21 % of the world’s total annual primary energy consumption ( (These figures are for 2006 – the most recent statistics I could quickly locate). Viewed from this perspective the U.S. appears to be a greedy, irresponsible consumer of diminishing resources.
Are we?
The short answer is … “no”.
A different perspective on this issue emerges when one considers the entire cost-benefit equation. According to Wikipedia (, referencing the Goldman Sachs International Monetary Fund, the U.S. generated 21% of the global GDP in 2008. Hmmmm, we consume ~ 21% of the annual primary energy and produce ~ 21% of the annual global GDP. So let's create a figure of merit... M = % Global GDP / % global energy consumption. M = 1 for the U.S.

What's the value of this figure of merit for the up-and-coming nations of the world… say India and China?
India has 1.17B people. China has 1.33B people. Total population = 2.5B. The same sources I cited above indicate China and India combine to consume 19% of the world’s total primary energy consumption in 2006, and produced 16% of the world’s total GDP in 2008. So M for India+China = 16% / 19% = 0.84. In other words, based on this figure of merit, India and China are less efficient at producing value from the energy they consume. Or, stated differently, they are consuming too much energy relative to the GDP they produce. But this is not, of course, the complete story. (More on that in future posts.)
So, while the average American consumes much more energy than the average citizen of India or China, each American also contributes much more “value” to the world economy.

“Visualization from Gapminder World, powered by Trendalyzer from“
It turns out there is a rather direct relationship between per capita energy consumed, and per capita GDP produced. This relationship is demonstrated rather dramatically by the plot above, which I generated at the wonderful website ( It displays national annual per capita GDP (Y axis) vs. per capita electric energy consumption in kWh (X axis) for the countries of the world. Gapminder is one of my favorite resources for visualizing world demographics data. I encourage everyone to check out their on-line data visualization tools. The plot vividly demonstrates the direct relationship between per capita GDP generation, and per capita electricity consumption. There are many other thought-provoking visualizations one can generate on the Gapminder site (the plot of UN Human Health Index vs. per capital electricity consumption for instance). All of these plots point to one fact: energy availablity is a key to quality of life and economic prosperity.
And what about entropy? Well, as those of you who've studied engineering or physics will recall, entropy is, among other things, a measure of disorder in a closed system. The higher the entropy, the higher the degree of disorder in the system. One of the interesting artifacts of the first and second laws of thermodynamics is that the application of energy is necessary to bring order from disorder. In a funny sort of way, this is what the plot shown above demonstrates - albeit from an economic perspective rather than an engineering perspective. Energy is required to bring order, organize matter, and add value from an economic perspective as well. The relationship is direct, strong, and unavoidable.
One important final note. All applications of energy are inefficient and imperfect. An our primary energy resources are limited. There are clearly economic advantages to be gained by taking steps to drive down energy consumption per unit of productivity delivered. The fact there is a very real relationship is not an excuse for waste and inefficiency, but rather a motivation for improving our energy usage efficiency.
Enough musing for now...


  1. That's a very interesting post, Sherrell, thank you!

  2. Sherrell,

    Good analysis. I have always argued that if politicians understood thermodynamics and used it to make decisions, we would be living in a better world.

    A discussion about energy and economics would be incomplete without including natural resources and the environment. It would be interesting to include a metric for sustainability and the impact of using certain types of fuels for producing electricity.
    For example. Let's consider the case of making silicon products for chips, which requires energy. The entropy of silicon in a chip is lower than its entropy when it was in the raw material. We use computers containing those chips to make goods that contribute to the GDP. But what about the entropy of the coal atoms that were use to generate electricity? What about the entropy increases associated with the mining of coal, the heat rejected during the entire process, the wear of machines and equipment, etc.
    We also need to account for the future unavailability of the coal that was used to generate that electricity. I would argue that if we extend the boundaries of our thermodynamic system to account for all these processes then there will be a decrease in sustainability and a net increase in entropy.

    I agree with your conclusion. What is interesting in the plot is that all the economies fall on the same line without saying anything about how energy-efficient they are. Would the slope of the master curve increase with increasing energy efficiency?


  3. Edgar,

    Great observations and comments!

    What you are describing is similar in many respects to the "life-cycle" environmental impact analysis that is commonly done for many human enterprises today. Llife-cycle CO2 emissions from electricity production being one example. I think the increment of value added at each step along the way would directly relate to an incremental entropy decrease. What if we could do a life-cycle entropy analysis in which we tracked the entropy change (much like value added) as a raw material moves through it's extraction - manufacturing - use - disposition life-cycle? How would we define the "system" boundaries?

    With regard to the slope of the curve, if we decrease our energy usage intensity or our energy efficiency without affecting our productivity, then the slope of the curve would change. Improving our energy efficiency in this manner would "bend" the curve downward. I personally feel those of us on the right-hand side of the curve had both the opportunity and the responsibility to do this. What I haven't thought about is the extent to which different approaches to reducing our energy usage intensity might simultaneously impact our productivity...