Economics and Entropy: Irreversibility


In the first part of this series readers were introduced to Nicholas Georgescu-Roegen, and the conditions by which economic value is created under entropy. In this part, I hope to outline and explain the first condition: Irreversibility.

One of the three important contributions that Georgescu-Roegen made that fundamentally connects the idea of the economy as a complex, adaptave system is the observation that processes that create economic value are inherently irreversible. Time in economic systems has a one-way arrow — you can’t burn the same gallon of gas twice. As we will see, economic value is created by humans taking unordered matter (natural resources), and through this irreversible process, creating goods and services which make us wealthier.

I define business as “a person, or group of people, who transform amtter, energy, and information from one state into another with the goal of making a profit.” Physical and social technologies can also be defined as transformations. The 19th century French engineer Sadi Carnot divided all transformations such as these into two categories; reversible and irreversible.

Be Kind, Rewind?

The earth orbiting the sun is an example of a reversible transformation (in the sense that it changes positions from point to point over time). There is nothing in physics that would lead anyone to believe that the current direction of the earth’s orbit is the only direction it could possibly go. Indeed, it could just as easily orbit in the opposite direction; and besides the change in seasonal patterns and the direction in which the sun rises, we would be none-the-wiser. If you saw a movie of the earth orbiting the sun in one direction, and then the other — with no prior knowledge — you would not be able to ascertain which direction was “backward”, as each would be perfectly symmetrical in time. Knowing the “correct” direction of the earths orbit requires a priori knowledge of a inertial frame of reference. There is no value created in the direction of the orbit of the earth.

In contrast, smashing a bottle of milk is an irreversible process. The Second Law of Thermodynamics gives time it’s arrow. Humans (and probably other life as well) intuitively understand that entropy increases over time, and that the only way to decrease entropy is through the application of energy (work). If we happened to watch a film of a milk bottle being smashed, or a drop of cream in a cup of coffee dispersing, we would see the order of those systems decreasing and know that time was moving forward. In experiments, if you were to find that milk bottles spontaneously reconstructed themselves, you would have a Type I Error on your hands, as this phenomenon does not occur in nature (or at least the probability is infinitesimally low, such that it would never happen in the lifetime of the universe). However, if we observed someone gluing the broken glass back together and refilling it, we would be observing energy being applied to the unordered system, and thus, time would be moving forward once more.

A useful way to think about order is to ask what the probability is of a particular state occurring at random. As an example, if you pour milk into a cup of coffee and let it sit without stirring it, eventually the milk will dissipate as the drink reaches an even temperature, and the molecules will return to a disordered state. You would obviously be quite surprised to look into your cup after a few minutes and find that the cup was perfectly ordered with coffee on one side, and the milk on the other (another one of those things that are theoretically possible, but with a “not in the lifetime of the universe” probability). Now imagine that there is a nano-divider in the cup, which is programmed to separate milk from coffee, and order each to one side of the cup. Over time, you would find that the previous scenario would, in fact, come to pass. The nano-divider is decreasing entropy in the cup of coffee by creating a lower-probability state than would have existed — but at the price of consuming energy and expending heat. This type of system is known as Maxwell’s Demon…but throughout the last century and a half, it has been concluded that Maxwell’s Demon cannot reverse entropy without a source of energy.

Is it possible for a value-creating economic transformation to be perfectly reversible? Charles Bennett devise the theoretical possibility of a reversible computer — a machine that can perform computations both backward and forward. This would obviously create immense economic value, and violate our first G-R condition! However, Rolf Laundaur has shown that such a computer would require infinite memory storage. As soon as memory needed to be erased, the computer would be carrying out an irreversible process. As long as there is a finite bound on possibility, then then our proposed condition is not violated.

Thus, when businesses transform disordered resources from the natural world into an ordered structure which can be consumed, they apply their energy (through work), and create economic value which is inherently irreversible. You can disassemble your vacuum cleaner into the sum of all of it’s parts, but it is very hard, and requires a great amount of additional applied energy to return the plastic to petroleum, or metal to ore.

No “Givesies-Backsies”!

So far we have covered production, but what about transactions, i.e. trade? “Traditional economics” states that trade is the result of people’s differing preferences; and that trade creates value by better matching resources with these preferences. If the first G-R condition is to hold, then we must show that value-creating trade is irreversible as well.

This is tricky from a thermodynamic perspective (Duncan and Foley 2002). However, intuition tells us that if two people agree to a trade because it is mutually beneficial, they will not immediately want to undo the trade. However, without an inertial reference frame, it is generally impossible to know whether the trade was forward or backward. Viewing a movie of two people trading marbles, red and blue, it is impossible for us to intuitively gather that the trade was “red for blue”, or the opposite. This requires an inertial frame.

Of course, if we asked a market researcher to survey the traders before and find out their color preferences, and the makeup of their marble collection, we could reasonably ascertain which way the trade was running[1]. We would also know that the trade created value by matching preferences with goods. However, only through the application of energy to the previously disordered situation would we be able to uncover these preferences, and know that neither party would want to immediately undo the deal.

Thus, irreversibility holds under value-creating trade, and is a necessary, but not a sufficient condition for value creation. Many irreversible processes are value-destroying: hurricanes, explosions, and (perhaps more pertinent to our times) incompetent management. All of these processes destroy value in ways that take energy to reverse. The first condition gives time an arrow in economies, but we need further conditions to give entropy an arrow, and specify ways in which we can further identify transformations and transactions that are value creating.

For the next installment in this series, see this article.
____
[1]Leo Szilard, whose theories were further developed by Leon Brillouin, showed that information acquisition inevitably results in a global increase in entropy.

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5 thoughts on “Economics and Entropy: Irreversibility

  1. The idea of irreversibility in economics is merely an analog to the second law of thermodynamics and should not be taken as homologous. The analogy is, however, useful, though I believe that irreversibility should be approached from an cognition and information theory perspective.

    http://nicoletedesco.wordpress.com/2011/06/25/cognitive-irreversibility-and-economic-value/

    The creation of information is strongly correlated with physical irreversibility. In economics, for about a hundred years now we have been correlating economic cost with degree of uncertainty. Committing to irreversible acts may reduce cognitive load by allowing information “compression” to occur. Concept formation may not be possible without the ability to let go of a state of indecision and “commit” to one cognitive structure or another. Cognitive irreversibility may be a strong motivating principle, whether explicit or implicit or simply an accidental epiphenomenon, in many cognitive processes. Cognitive irreversibility may provide a “ratchet effect” which allows us to arbitrate confusion, gain knowledge through symbolic processing and drive social behavior.

    I am still working on precision with this principle. However, given my background in physics I am quite conscious of when I am borrowing an analogy and when I am not.

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