Sunday, June 5, 2011

There is no Energy or Exergy Crisis. It's a Problem of Low Rates of Return on Investment. Understanding the Problem by Correctly Defining Energy, Exergy and Entropy

"The first step to wisdom is getting things by their right names."  Chinese saying quoted in E.O. Wilson's Consilience and books by D.S. Scott

The Earth is a system far-from-equilibrium. It is continuously bathed in a source of exergy (available work) in the form of sunlight. Life on earth does not suffer from a lack of potential exergy sources. This means that we are nowhere near the limit of how much exergy we can extract from sunlight, and likewise we are nowhere near the limit of how much exergy can be extracted from fossil fuels, wind, geothermal or nuclear fusion/fission. The global ‘energy’ problem we face is not due to a lack of exergy, both of which are plentiful (for example, visit this link to The Earth’s Exergy Balance), but rather it is associated with the increasing cost to generate useful forms of work, such as electricity and movement of transportation vehicles. The increase in cost is in part due to the increasing depths required to drill for oil/natural gas, the decreasing reserves of cheap, light, sweet crude oil, as well as the uncertainty surrounding the global environmental impact of our exergy consuming processes (automobiles, power plants, etc…). It is also in part due to incorrect understandings of the second law of thermodynamics that have propagated in the West regarding minimizing exergy consumption and entropy production (i.e. we have a philosophical problem in the West in which we think that minimization exergy consumption is a good thing.) This misunderstanding came from faulty extrapolation from early work by Ilya Prigogine in the area of 'linear' non-equilibrium thermodynamics. The goal of this post is to correct some of the misunderstandings surrounding energy, entropy and exergy so that we understand the real problem we face here on Earth (our lack of growth in the West).

The simplest, but still correct, statements regarding exergy and energy are: Exergy is consumed. Energy is always conserved. Both exergy and energy have units of energy (such as kW-hrs or BTU’s or kJ’s). Energy is always conserved (even in nuclear reactions) and the conservation of energy can be derived using Noether’s Theorem when there is a symmetry of shifting time (meaning I can run my isolated experiment on Tuesday or Wednesday, and as long as the starting conditions are the same, I will get the same results.) Exergy consumption (i.e. exergy decreases globally with time) is due to the non-conservation of entropy. Entropy is not a conserved quantity, and this can be related to the fact that there is no mirror symmetry for time (i.e. you can’t run your experiment backwards and obtain the same result.) So, we live in a universe with a time shift symmetry, but not a time flip symmetry. The time shift symmetry leads to the First Law of Thermodynamics and the non-existence of a time-flip symmetry leads to the Second Law of Thermodynamics. Exergy is defined as the maximum amount of work that can be derived from a fuel/material by bring it into equilibrium with its environment. The exergy balance equation can be derived by multiplying the equation for the Second Law of Thermodynamics by the temperature of the environment and subtracting it from the equation for the First Law of Thermodynamics. If you’re interested check out:


As state earlier, we don't consume energy. Energy is conserved in all known processes. For example, there isn't any less energy in the universe after you use up all of the gasoline in our cars. All we do is convert one form of energy into another, such as converting the directed kinetic energy of the wind into electricity via a wind turbine. Or inside of a nuclear reactor, we convert nuclear potential energy into thermal energy of steam so that we can use a steam turbine to convert the thermal energy of the steam into electrical energy. The total amount of energy is always the same.

But there's more to it than just energy conservation.  There's also entropy production, i.e. the non-conservation of entropy. Entropy has a scale from zero to infinity in the same way that temperature has a scale from zero to infinity. Certain forms of energy with lots of entropy (such as thermal energy) cannot be converted completely into low entropy forms of energy (such as potential energy.) A pot of water cannot spontaneously cool itself and raise itself in a gravitational field, even though such a process could conserve energy. Stating the second law of thermodynamics another way, there's no way for regenerative brakes to recover 100% of the directed kinetic energy of the car.

I’d also like to focus here on what entropy is and what it is not. It’s been a perpetually propagated myth that entropy is equal to disorder. This is an incorrect statement that continues to be propagated because the real definition of entropy is pretty much impossible to convey to anybody who hasn’t taken a course in statistical mechanics. Entropy does not mean disorder and it does not mean a lack of structure.  I’m not even sure how one would quantify disorder or lack of structure. Unlike a term like disorder, entropy is measurable and countable. The technical definition of entropy is: a constant times the logarithm number of equivalent microstates (i.e. positions and velocities of particles) that yield the exact same macrostate (i.e. temperature and pressure) for the macrostate with the most microstates. (The technical definition might be tough to follow if you haven’t taken a course in statistical mechanics, but please bear with me because it's important to use correct definitions as much as possible.)   I am now going to attempt to explain entropy in non-technical terms, but in terms that are measurable and countable (unlike disorder). If instead one tries to describe entropy in terms that are non-measurable and non-countable, then one is misrepresenting entropy and is describing something else altogether.

We need to stop thinking about entropy as disorder; instead entropy is related to the concept of permutation symmetries. (As explained best by Joe Rosen in any of his books.) A macrostate with N number of microstates is symmetric (i.e. doesn't change) under the operation that is a member of the permutation group S sub N. The size of the symmetry group S sub N is equal to N!  (N factorial...which is an absolutely huge number because N itself is absolutely huge.) The underlying reason why we can swap the different microstates and not change the macrostate is that the particles (with the same numbers of protons, neutrons & electrons in the same energy & spin states) are indistinguishable at the quantum level. So, as the entropy of the system increases, so do the underlying number of symmetry operators. There is a one-to-one and monotonically increase relation between the number of microstates and the number of permutation symmetry operators. This means that the entropy of the system is intimately connected with the number of permutation symmetries of the constituent microstates. This is why I stated that entropy is real, measurable and countable (and therefore entropy should not be confused with disorder.) Because entropy is a countable number, it is a dimensionless variable; it has no units. However, since this number would be absolutely huge for systems of importance, engineers and scientists have decided to take the logarithm of the number of microstates, and to multiple the dimensionless logarithm by Boltzmann’s constant (1.3 *10^-23  J/K). Or by including Avogadro’s constant, the units of entropy become the same as the universal gas constant (J/mol*K). And note that these permutation symmetries aren’t the spatial symmetries which many of us are familiar with or the time symmetries mentioned above. These are permutation symmetries of exchanging exactly similar, indistinguishable particles.

As the entropy (i.e. the number of microstates of the current macrostate) increases, so does the number of permutation symmetries. The second law is therefore a statement that the permutation symmetries of the future will be equal to or greater than the number of permutation symmetries of the past. As stated in the Curie-Rosen Principle, "The symmetry of the effects has to be higher than the symmetry of the casuses." Or as technically stated in many of the books by Joe Rosen, "The symmetry group of the cause is a subgroup of the symmetry group of the effect." This means that the second law of thermodynamics is really a statement about the total symmetry of the future in relation to the total symmetry of the past. Not only does the future have to contain the symmetries of the past, but might have more symmetries. Stated again, the future at least as symmetric as the past. Any symmetry in the past must persist into the future, and new symmetries can be made. We'll see that new symmetries can be made due to irreversible processes.

The Second Law of Thermodynamics is a sub-set of the more general Curie-Rosen Principle for the case of the type of permutation symmetries that are called the entropy of a system. Stated again, the Second Law of Thermodynamics is a statement that the future will have at least as many permutation symmetries as the past.

Note: One might think that the Curie-Rosen Principle is false because living dissipative structures, such as bacteria or humans, as well as non-living dissipative structures, such as Rayleigh-Benard convection cells or tornadoes, apparently break spatial symmetry (and hence would violate the Curie-Rosen Principle) when they form. But this is not the case. The Curie-Rosen Principle ends up stating that the family of solutions to any differential equation contains the symmetries of the differential equations themselves. Any particular solution (such as whether the Rayleigh-Benand convection cell rotates clockwise or counter-clockwise) depends on initial conditions that can never be perfectly symmetric.

So, what prevents convection cells from always occurring? The circular motion of Rayleigh-Benard cells is a form of directed energy (i.e. exergy). The entropy of directed motion is zero. Bernard cells can not form spontaneous in equilibrium. Instead, there must be a gradient in temperature to drive the process. The temperature on the hot side can be considered to be a form of exergy. The exergy in the heat input must be greater than the exergy in the motion of the cells. The formation of convection cells will only occur if the heat transfer (and hence the entropy generation inside system) is greater than the heat transfer via heat conduction alone. The convection cells will amplify a near-symmetry into a clear non-symmetry only if it can increase the production of entropy (and hence the production of permutation symmetries.) The convection cell (or any biological cell for that matter) increases the entropy of the universe.

Life processes increase the entropy of the universe because they are capable of catalyzing chemical reactions (i.e. consuming exergy) that might not occur within the next billion years (because of activation barriers to the chemical reactions.) Interestingly, the amplification of near-symmetry into clearly broken-symmetry by life processes is a self-replicating process because some of the exergy derived from the chemical reactions goes into looking for more exergy and some of it goes into replication (i.e. more breaking of spatial symmetry). I'm not sure that I would classify a Rayleigh-Benard convection cell as a self-replicating processes.

Now, after having discussed entropy and how it is related to permutation symmetries and how it is not conserved, we can see that any quantity like exergy (which is derived from the second law of thermodynamics) will not be conversed. In fact, the exergy of an isolated non-equilibrium system decreases as the entropy increases. In precise terms, the entropy production of an isolated system is equal to the amount of exergy destruction divided by the reference temperature of the environment. Or we could say the same thing in reverse. The amount of exergy destruction is equal to the amount of entropy production multiplied by the temperature of the reference environment.

The term now called ‘exergy’ used to go by the name ‘availability.' The reason why the term ‘availability ' is falling out of favor with engineers is that this name gets easily confused with the term ‘availability’ in the sense of: ‘is the power plant online and available to produce power?’ The term ‘exergy’ was first coined in 1953 by Professor Zoran Rant. From Greek origins, we have: ‘ex’ = out of   &  ‘erg’ = work.   i.e. 'work out of.'   What Prof Zoran Rant was trying to convey was that exergy measures the maximum amount of “work” that can be extracted “out of” a fuel/material during a reversible process that brings the fuel/material into equilibrium with the environment.

The units of exergy are kW-hr, and the value of exergy can either be zero (when the fuel/material is in equilibrium with the reference environment) or positive (when the fuel/material is not in equilibrium with the reference environment.)  The exergy of a fuel/material cannot be negative. (Just like the fact that there is no such thing as negative entropy or negative entropy production.) A vaccum has positive exergy with respect to the environment just as a pressure cylinder has positive exergy. The direction of motion of the piston is in opposite directions, but work can be derived from the direction of motion of the piston in either case, and converted into electrical energy, and then sent far-away so that it doesn’t matter which way the piston moved when generating the work. The same holds true for materials that are colder than the reference environment. The exergy is still positive.

One must be careful with the definition of exergy because our reference environment is not in equilibrium. For example: 1) The relative humidity of the environment is hardly ever 100%. The amount of water vapor in the atmosphere can sometimes be greater than 100%, but most of the time, it’s less than 100%. This is a good thing because our bodies rely on perspiration in order to cool ourselves. 2) The amount of methane in our atmospheric greater than it should be if our atmosphere were in thermal equilibrium. So, we should not use the atmospheric amount of methane in calculations of the exergy of compressed methane. Another problem with exergy is that it's often hard to know what the reference environment is because the temperature and composition of the atmosphere changes all of the time.

This means that exergy is not a fundamental quantity, even though it is particularly useful to our understanding of what happens when we burn gasoline in cars or natural gas in a gas turbine. We are consuming exergy, not energy. But as I stated earlier, we are not running out of exergy sources (The Earth’s Exergy Balance). There are plenty of exergy sources that we could use to power our vehicles or power plants.

The problem is that our rate of return on investment is low (except in China and India). As I showed in a previous post (The Wealth of Nations or Updated Here), there has been essentially no growth in the major economies between 2000 and 2009 (except China and India) when measured in inflation-adjusted units, such as the generation of work in kW-hrs. For example, the US has had an average rate of return on work invested of 0.0% between 2000 and 2009.

This means that the US economy has not been growing, and this is a problem because the goal of life is to increase the entropy and hence the underlying symmetry of the universe.

What we need to do is to improve the rate of return on work invested that goes into building and operating our power plants and our transportation vehicles. This is the only way to achieve growth, to increase our production rate of entropy, and hence to increase the production rate of permutation symmetries in the universe.

Of course, we have to be smart about growth. We have to have growth that doesn't come at the expense of future growth. For example, one could build a high rate of return on investment power plant with minimal safety features, but this might end up being harmful to humans and the environment, and might end up causing a decrease in future growth, such that a more safe power plant would end up having the higher average rate of return on investment. (The Tortoise and the Hare comes to mind here.)

And this is the essential human dilemma, how to achieve balanced growth? As a world, we don't seem to have the right answer to this question. In China, there is growth, but it is often at the expense of future growth because of the sheer amount of pollution being created. And in the West, there is no growth, and hence there's stagnation.

We need to figure out how to achieve a balance between the "growth without human or environmental rights" in China and the "no growth but human and environmental rights" in the West. In the The Wealth of Nations post, a figure shows that India's 5%/y average growth rate is in the middle between the 11%/yr growth in China (where they don't have any fundamental human rights) and the 0%/yr stagnation in the West (US=0.0%/yr, Germany & France = -0.1%/yr, and Japan = -0.4%/yr between 2000 and 2009.) And perhaps this is no coincidence. In general, India seems to have a philosophy of life some place in between that of China and the West. Perhaps there's something for all of us to learn about how India balances current growth with future growth. Or perhaps there is something to learn from what's good and what's bad about all of the major cultures.

But since the future is unpredictable, there is no right answer to the question "how to expand life in the fastest possible way?". History is not for us to duplicate, but rather, it's a guide for us learn and improve.

In summary, we do not have an energy problem because energy is always conserved (i.e. the energy of the universe is a constant). And we do not have an exergy problem because we are not lacking potential exergy sources.  But we do have a rate of return on investment problem because it's more difficult or expensive to reach exergy sources and because we seem to have come under the spell of certain philosophies of life that tell us to minimize the consumption of exergy.

Since the goal of life is to grow, we need to tackle both of the major causes of our lack of growth in the West. This means changing our underlying philosophy of life in the West so that we chose technologies that achieve high overall, average rates of return on investment  (such as natural gas combined cycle in the US, perhaps nuclear in France, and perhaps coal with acid and greenhouse gas capture/sequestration in China) and avoid low rate of return on investment technologies, such as wind and solar (until they can demonstrate high rates of return on investment as a baseload electricity sources.) We need to consume exergy sources in such a way as to achieve a high rate of return on investment and, in this way, we achieve nature's goal of increasing the underlying symmetry of the universe.


  1. Thank you for a very interesting article, but when you promote continuos growth on fossilised solar exergy it demonstrates that you haven't understood the origins and evolution of life to its today's homo economicus. The earth system has not evolved to dissipate a myriad of solar exergies (current and fossilised), the overshoot of entropy (since the industrialization) is resulting in a changing climate, severe loss of biodiversity and hence in dysfunctional ecosystems, which still and will sustain any economies (whatever sectors). Secondly, Nature is not expanding or growing as you say, it is indeed creating more entropy than without its existence as it tend to become more complex and diversified, but it has a limit to its wealth, which is a typical mature ecosystem (e.g. forest ) bounded to the exergy received to earth surface. So the belief in an ever expanding economies/societies is a common shibboleth of neoclassical economists or optimist technologist. Remember that the economic system is a subsystem to the earth system, and will depend not only on the exergy availability (which is indeed, as you say, not in a lack of) but how much entropy is created through the use of exergy, and the entropy the atmosphere and biosphere can handle without disrupting life too severely as it has happened in the past with high carbon concentration. Even more urgently the disorder of matter, to which the earth is a closed system, is ever increasing in human societies. In nature, the disorder of matter is closed to constant (depending on the time frames of your system), as it is recycled over and over again, through the natural cycles of life, and powered by natural solar exergy! In human societies this waste (by product of fossilised exergy- extraction of coal, oil and gas) is also disrupting the resilience of ecosystem, hence of human systems as well I am happy if this could open a discussion !

  2. Anonymous, thank you for your comment. This blog is intended as a place to discuss these ideas openly.

    As you can see from this post or other posts on this website, my philosophy is that the goal of life is to expand. This includes both expanding to other planets and further growth on this planet (i.e. we are no where near using all of the exergy available from the Sun.)

    I have come to this philosophy from my understanding of systems far-from-equilibrium.

    It would be easier for me to respond to your comment if I knew what your philosophy of life is. What you do think is the goal of life?

    So, if you give me some background on your philosophy of life, I'd like to see if we share the same goal of life (and differ on how to achieve that goal of life) or whether we have completely different ideas about the goal of life.

  3. "The technical definition of entropy is:" Not quite, you left out the logarithm, which is necessary for a very informal description, but when you say "THE TECHNICAL", then leaving it out is a sin. Might as well go all the way and specify that you're talking about thermodynamic entropy and include the constant.

    "And we do not have an exergy problem because" This seems like an equivalent level of debate to "Guns don't kill people." I can't really see what progress there is in semantically wrangling the point that we all say "energy problem" instead of the more correct but tiresomely pedantic: "problem accessing energy affordably".

  4. Ron,
    You are correct. The technical definition of entropy is a constant time the logarithm of the number of equivalent microstates, and I have fixed this in the post. If you read some of my other posts, you see that sometimes I give the full definition of entropy and sometimes I get lazy and ignore the logarithm and the constant for the sake of simplicity. But given that this post is about getting definitions correct, you are correct in calling this a "sin."

    The goal of this post is to define the problem: The problem is a lack of economic and population growth...not energy and not exergy.

    I think that it's crucial to define the real problem, or else people will come along with supposed solutions to the "energy problem," which turn out to make growth rates even lower (such as many wind, solar, and biofuel projects.)