Is recycling possible?


Georgescu-Roegen coined the fourth law of thermodynamics according to which matter continuously and irrevocably degrades from an available to an unavailable state in a closed system including the Earth and predicted that we would soon arrive at the state of maximum entropy, material death rather than heat death. He also insisted that recycling could not avoid this material death, because the ideal of complete recycling is based on the illusion of the thermodynamically impossible perpetual motion. But what he called the fourth law of thermodynamics is false. A closed system such as the Earth can reduce material entropy in exchange for increasing thermal entropy, keeping the former low by dumping the latter in outer space. That is to say, the sustainable economy based on recycling is possible, at least theoretically.


1 : What is the problem of the modern economics?

According to Nicholas Georgescu-Roegen (1906 – 1994), classical and neoclassical economics is mechanistic in the same sense in which we generally believe classical mechanics to be.

Classical mechanics is mechanistic because it can neither account for the existence of enduring qualitative changes in nature nor accept this existence as an independent fact. Mechanics knows only locomotion, and locomotion is both reversible and qualityless. The same drawback was built into modern economics by its founders, who, on the testimony of Jevons and Walras, had no greater aspiration than to create an economic science after the exact pattern of mechanics.[1]

To be sure, Adam Smith published The Wealth of Nations, the monumental work of classical economics, in 1776, after the 17th century scientific revolution, with his theory showing a similar tendency to classical mechanics; just as Newtonian mechanics used a mechanistic model of bodies with mass and the force exerted on them, classical economics used a mechanistic model of individuals with self-interest and the motivation to maximize their utility. As William Stanley Jevons (1835 – 82) once expressed, modern economics is the mechanics of utility and self-interest[2]. Both Newtonian mechanics and classical economics presupposed a reversible super-historical mechanism, ignoring the irreversibility of time.

A glaring proof is the standard textbook representation of the economic process by a circular diagram, a pendulum movement between production and consumption within a completely closed system. The situation is not different with the analytical pieces that adorn the standard economic literature; they, too, reduce the economic process to a self-sustained mechanical analogue.[3]

Although the 17th-century scientific revolution was the revolution of physics in essence, it started from the field of astronomy. This was because the movement of heavenly bodies is free from turbulent factors such as air resistance and friction which prevent physicists from constructing a simple theory of mechanics from terrestrial observation. It was because of its regularity that Johannes Kepler was able to discover the laws of planetary motion. Newton applied the ideal laws of the celestial realms to the terrestrial realms and established the law of universal gravitation. He completed a new paradigm of making the entire world into a reversible super-historical machine. Naturally, the new paradigm was soon applied to the field of economics.

Meanwhile, a new field of physics, thermodynamics, appeared that focused rather than ignored heat generated from friction. Though the first model of thermodynamics, Carnot Cycle, was an ideal reversible cycle which ignored turbulent factors, Carnot’s theory eventually resulted in the discovery of the second law of thermodynamics that attested to the irreversibility of physical process. Even after the discovery of the law of entropy, economists have adhered to Newton’s paradigm and held timeless economic theories that presume the endless exploitation of resources.

Of course, there were some economists who affirmed the irreversibility of history. The most famous is Karl Marx. But history for Marxists was progress, not regress. Marxist economics is not different from classical economics in the optimistic assumption that economy would grow unlimitedly. In spite of his criticism against classical economics, Marx succeeded to their labor theory of value and did not ascribed value to natural resources. But according to the law of entropy humans can only consume the value produced by nature, or strictly speaking, we consume more than we can produce. That is to say, we will come to an end, wasting away the entire resources available. The future was bright for Marx and other economists who thought workers could produce more value than they consumed, but gloomy for Georgescu-Roegen. That is why he thought Marx was not beyond the boundary of the previous economics.

Though his approach is different from that of Marxists or modern economics, he had some predecessors. Some economists paid attention to the second law of thermodynamics and tried to introduce the concept of entropy into economics. Harold Davis (1892-1974), an American mathematician, seeking to establish a formal similarity between the fundamental thermodynamic equations and some equations used in economic models, suggested in his 1941 discussions that the utility of money should be economic entropy[4], but none of the variables used in the mathematical economic models played the same role on entropy in thermodynamics[5].

In addition, Kenneth Ewart Boulding (1910 – 1993) in his book in 1964, The Meaning of the Twentieth Century; the Great Transition, warned that the entropy trap[6] would prevent the great transition from a civilized to a post-civilized society, but Georgescu-Roegen did not mention him, probably because Boulding was too near him.

According to Georgescu-Roegen, however, the thermodynamic approach had already been introduced into economics from long ago, because the founder of thermodynamics, Carnot, could be regarded as an economist.

In retrospect it is obvious that the nature of the problem in which Carnot was interested is economic: to determine the conditions under which one could obtain the highest output of mechanical work from a given input of free heat. Carnot, therefore, may very well be hailed as the first econometrician.[7]

Of course, none of Carnot, Clausius or Boltzmann had ever grappled with economics proper. That is why Georgescu-Roegen’s attempt came into the spotlight.

2 : Do natural resources have no value?

Georgescu-Roegen questioned that the conventional economists did not evaluated natural resources as if they were inexhaustible.

The intriguing ease with which Neoclassical economists left natural resources out of their own representation of the economic process may not be unrelated to Marx’s dogma that everything nature offers us is gratis.


Perhaps the absence of any difficulty in securing raw materials by those countries where modern economics grew and flourished was yet another reason for economists to remain blind to this crucial economic factor. Not even the wars the same nations fought for the control of the world’s natural resources awoke economists from their slumber.[8]

Then he mentioned as an exception The Coal Question: An Inquiry Concerning the Progress of the Nation, and the Probable Exhaustion of Our Coal-Mines that Jevons published in 1865 to warn that the supply of coal in Britain was running out. He had a pessimistic prospect that improvements in fuel efficiency of steam engines would increase rather than decrease fuel consumption[9].

Another exception was David Ricardo (1772 – 1823). In his book The Principles of Political Economy and Taxation in 1817, he distinguished natural resources such as coal from the original and indestructible powers of the land[10]. The power differs from land to land and the land of a higher quality is limited. Ricardo ascribed rent to the difference in the quality from the poor land you can use for free. It is called Ricardo’s cost-difference theory of rent.

Both Ricardian land and the coal deposits are available in limited amounts. The difference is that a piece of coal can be used only once. And, in fact, the entropy law is the reason why an engine (even a biological organism) ultimately wears out and must be replaced by a new one, which means an additional tapping of environmental low entropy.[11]

Suppose you use a portion of land as a farm, for example. Crops can produce low entropy resources from the temperature difference between the hot heat reservoir that the sun makes and the cold heat reservoir that transpiration makes, storing it in the form of organic matter. Coal also originates in ancient plants. Organic matter including fossil fuels loses its resource value, when burned, but the Earth as a heat engine continues to create new organic matter on your farm. Land seems to have permanent value because the Earth as a heat engine is expected to create economic valuables such as organic matter. Without this expectation land cannot have any permanent value.

The conventional economists did not think so. Both classical and Marxist economists assumed that the source of the economic value would be attributed to human labor. Certainly it is humans that set the price of a commodity, but it is thermodynamically false to hold that human labor can create economic value physically from nothing. What creates the terrestrial value is the Earth as a heat engine and, as humans produce more entropy than value, it follows that we consume rather than produce value. The reason we nevertheless tend to feel we are creating positive value is that we just forget the entropy we throw away into outer space. All we can do at best is to avoid waste at work.

3 : What relation does the economic value have to entropy?

As I asserted previously, there are two price-setting factors in a commodity, its usefulness and scarcity, both of which can be explained in terms of entropy[12]. Georgescu-Roegen gave up defining value in general by entropy and confined himself to admitting that low entropy is a necessary condition for a thing to be useful.

Casual observation suffices now to prove that our whole economic life feeds on low entropy, to wit, cloth, lumber, china, copper, etc., all of which are highly ordered structures. But this discovery should not surprise us. It is the natural consequence of the fact that thermodynamics developed from an economic problem and consequently could not avoid defining order so as to distinguish between, say, a piece of electrolytic copper ― which is useful to us ― and the same copper molecules when diffused so as to be of no use to us. We may then take it as a brute fact that low entropy is a necessary condition for a thing to be useful.[13]

He thought low entropy was merely a necessary condition and not a sufficient condition for a thing to be useful, because poisonous mushrooms have low entropy but are not useful or omelet has more entropy but more usefulness than an intact egg[14]. If high entropy omelet is more useful than low entropy egg, then low entropy is not even a necessary condition. Moreover, diluting a poison so as not to cause damage to humans makes it valuable, although dilution increases entropy.

His attempt to connect usefulness with entropy itself is not wrong, but, as he did not understand that the usefulness of a commodity depends not on the low entropy of the commodity itself but on the causal contribution to the reduction in entropy of the subject that evaluates it, he made a mistake at the conclusion. The scarcity of a commodity is entropy as uncertainty of availability and it has the more value the more uncertainty its availability negates. Georgescu-Roegen, who condemned the connection between information and physical entropy as misleading[15], could not accept the definition of entropy as scarcity. For him it is either heat or material dissipation.

4 : Is the complete recycling impossible?

Entropy is a thermodynamic concept. Clausius first defined it only in terms of heat and temperature, but later redefined it as the entire transformation value of heat and disgregation (dissipation). Georgescu-Roegen, inventing a slogan Matter matters, too[16], laid more emphasis on disgregation than on heat. He thought the second law of thermodynamics is perceived to describe only the increase in heat entropy and coined additional law, the fourth law of thermodynamics concerning disgregation entropy, No closed system can perform mechanical work at a constant rate indefinitely[17].

The implication is that, in a closed system, matter continuously and irrevocably degrades from an available to unavailable state. A closed system that can perform mechanical work steadily constitutes perpetual motion of the third kind.[18]

He had already anticipated the discovery of a fourth law of thermodynamics as a thermodynamic clock[19] in his book published in 1966 and alluded the clock would point to another end different from the heat death.

According to statistical mechanics, therefore, the degradation of the universe would be even more extensive than that envisaged by Classical thermodynamics: it covers not only energy but also material structures. As physicists put it in nontechnical terms, In nature there is a constant tendency for order to turn into disorder. Disorder, then, continuously increases: the universe thus tends toward Chaos, a far more forbidding picture than the Heat Death.[20]

Georgescu-Roegen first stated the law in A Different Economic Perspective read at the AAAS (American Association for the Advancement of Science) Meeting, 18-24 February 1976. The closed system that the fourth law is applied to is a system that exchanges not matter but energy with the environment and the Earth is such a system. Since heat caused by solar radiation is discarded into outer space, the Earth can exchange energy with its environment. But unlike heat, matter can hardly be discarded into outer space. While light molecules such as hydrogen and helium can break free of the gravitational pull, other heavy matter, say rockets, cannot escape from the Earth without consumption of much energy. Some substances such as a meteorite flow into the Earth from outer space. Since we can neglect these quantitatively minor exceptions, we can safely say the Earth is close to a closed system, if not a completely closed one. Therefore unlike thermal entropy, material entropy cannot be easily cast away from the Earth. That is why Georgescu-Roegen thought that we would arrive at the material death before the heat death.

A perpetual motion machine of the first kind violates the first law of thermodynamics (the law of conservation of energy) and a perpetual motion machine of the second kind violates the second law of thermodynamics (the law of increasing entropy). Georgescu-Roegen named a perpetual motion machine that violates the fourth law of thermodynamics (the law of matter dissipation) “a perpetual motion machine of the third kind” after the conventional ones. According to him trying to implement complete recycling is an attempt to create a perpetual motion machine of the third kind, which is destined to fail. He explained why the complete recycling is impossible as follows.

Unquestionably, with a little effort we can reassemble all the pearls of a necklace that has broken inside a room, even in a hall. But to perform the same feat for a collier that has broken somewhere in Manhattan, it would take not only a fantastic amount of energy, but also a long, very long, time. In this long process, some material devices (shoes, for instance) will wear out and will have to be reassembled thereafter; we will be involved in a virtually endless regress. However, even this second story does not depict the actual dissipation of matter. Dissipated matter is most vividly illustrated by the copper molecules detached by use from a worn-out penny, by the rubber particles detached from worn-out tires, by the molecules of carbon carried by the exhaust of an automobile into the atmosphere. We are often told that in every human’s breath there is now a particle of air that was once breathed by Plato. More in the interest of the present time, we know that some dangerous radioactive elements have ultimately contaminated the milk of large areas. Can we reassemble them all only by the use of energy and thus render the milk safe to drink? Can we reassemble them at all?

By an unwarranted extrapolation from macroscopic to microscopic structures and by ignoring the endless chain of the additional wear-and-tear caused by recycling even broken necklaces, one is apt to proclaim that recycling can be complete. The bare truth is that the rubber molecules detached by use from tires on the roads are irrevocably lost. The complete recycling of these materials, even if envisioned as Gedankenexperiment, would require a fantastically long time, virtually infinite. This obstacle alone could not be overcome by our finite existence, which (as mentioned earlier) is the same reason that denies the possibility of complete reversibility.[21]

This explanation shows how he misunderstood recycling. It will surely require unlimited energy and time if you should number all the copper atoms detached by use from a worn-out penny, recollect them and restore them to the original position. But this is not what we call recycling. Recycling is not the restoration of the same thing but new production of a similar thing. Unlike the former, the latter requires limited energy and time.

Georgescu-Roegen, invoking statistical mechanics, redefined the concept of entropy as if he could have exceeded the limits of Clausius. But Clausius had already distinguished between thermal entropy and dissipation entropy, recognizing that the increase in the former could compensate for the decrease in the latter[22]. A closed system such as the Earth can reduce dissipation entropy in exchange for increasing thermal entropy, keeping the former low by dumping the latter in outer space. The universe is so large that we do not have to worry about the increase in entropy of the entire universe. So, the fourth law of thermodynamics is false and recycling is not a perpetual motion machine of any kind.

5 : How does the Earth recycle resources?

Georgescu-Roegen’s prediction of material death of the Earth in the near future is based on the idea that nature does not reproduce material resources.

Man’s natural dowry, as we all know, consists of two essentially distinct elements: (1) the stock of low entropy on or within the globe, and (2) the flow of solar energy, which slowly but steadily diminishes in intensity with the entropic degradation of the sun.[23]

A dowry is the money or property that a wife or her parent gives to her husband at her marriage. It is transferred only once, never to be supplemented. Such was Georgescu-Roegen’s interpretation of low-entropy resources on or within the globe. He explained the difference of two distinct sources from which the free energy available to us comes as follows.

Man has almost complete command over the terrestrial dowry; conceivably, we may use it all within a single year. But, for all practical purposes, man has no control over the flow of solar radiation. Neither can he use the flow of the future now. Another asymmetry between the two sources pertains to their specific roles. Only the terrestrial source provides us with the low-entropy materials from which we manufacture our most important implements.[24]

If solar radiation is flow, so is terrestrial heat. Neither flow of the future can we use now. The former flow increases the low-entropy stock of organic matter, while the latter flow increases the low-entropy stock of mineral resources. Unlike dowry, these resources are not one-off, one-shot stock. The work of the Earth as a heat engine continuously reduces the entropy of dissipated materials and reproduces new stock.

The old products of photosynthesis, when they went underground, are called fossil fuels, as if they were not renewable. The photosynthesis, however, recycles carbon dioxide and water that combustion of fossil fuels discharges into the organic matter. It is called biomass, but, as there is no essential difference between biomass and fossil fuels, they should be considered to be sort of biomass. It means fossil fuels are renewable energy resource. Today we should be worrying about the exhaustion of fossil fuels, not because they are not renewable resources, but because the speed at our consuming fossil fuels exceeds that of their production. This is a matter of quantity and we cannot conclude from it that the theoretical impossibility of recycling. If we consume as much as plants produce, the fourth law of thermodynamics will not hold true.

How about another “natural dowry,” mineral resources? Its entropy does not irreversibly go on increasing any more than that of biomass resources. A mixture of mineral resources melts and crystallizes through magmatic processes or hydrothermal processes to form an underground or undersea deposit. Wind and rain can smash a mixture of mineral resources and transport its pieces through surficial processes to form placer deposits, laterite deposits and residual deposits. These works of the Earth as a heat engine reduce the dissipative entropy of mineral resources. The fourth law of thermodynamics is false as to this stock, too.

Of course, the speed of the Earth’s reduction of mineral entropy is low. According to the observation on lavas of Mauna Loa shield volcano, Hawaii[25], the cycle of subduction and upwelling of the crust is 200–650 million year long and the average speed of general mantle circulation is about 2 (±1) cm per year. Though upwelling of mantle would form new magmatic deposits, the speed at the mantle convection reducing mineral entropy is far lower than that at our increasing its entropy. Therefore, while we should endeavor to decrease the speed of consumption, we must introduce the works of the Earth as a heat engine, such as smash and concentration, melting and crystallization, into our disposal of waste. While the speed of natural recycling of organic substances is much higher than that of mineral resources, we can artificially accelerate and control the recycling by means of agriculture. In addition to natural recycling, artificial recycling is at least theoretically possible.

6 : References

  1. The Entropy Law and the Economic Process (page) 1 (author) Nicholas Georgescu-Roegen
  2. The Theory of Political Economy (page) 21 (author) William Stanley Jevons
  3. The entropy law and the economic problem (author) Nicholas Georgescu-Roegen (media) Valuing the Earth: Economics, Ecology, Ethics (page) 75 (editor) Herman E. Daly, Kenneth N. Townsend
  4. The theory of econometrics (page) 171-76 (author) Harold Thayer Davis
  5. The Entropy Law and the Economic Process (page) 18 (author) Nicholas Georgescu-Roegen
  6. The Meaning of the Twentieth Century; the Great Transition (chapter) 7 (author) Kenneth Ewart Boulding
  7. Analytical economics: issues and problems (page) 92 (author) Nicholas Georgescu-Roegen
  8. The Entropy Law and the Economic Process (page) 2 (author) Nicholas Georgescu-Roegen
  9. The Coal Question: An Inquiry Concerning the Progress of the Nation, and the Probable Exhaustion of Our Coal-Mines (page) 4 (author) William Stanley Jevons
  10. The Principles of Political Economy and Taxation (chapter) 2 (author) David Ricardo
  11. The entropy law and the economic problem (author) Nicholas Georgescu-Roegen (media) Valuing the Earth: Economics, Ecology, Ethics (page) 80 (editor) Herman E. Daly, Kenneth N. Townsend
  12. What is Value? (author) Nagai Toshiya
  13. Analytical economics: issues and problems (page) 93-94 (author) Nicholas Georgescu-Roegen
  14. The Entropy Law and the Economic Process (page) 282 (author) Nicholas Georgescu-Roegen
  15. Ignorance, Information, and Entropy (media) The Entropy Law and the Economic Process, Appendix B (page) 388-406 (author) Nicholas Georgescu-Roegen
  16. Matter matters, too (author) Nicholas Georgescu-Roegen (media) Prospects for Growth: Changing Expectations for the Future (page) 293-313 (editor) Kenneth D. Wilson
  17. Energy and matter in mankind’s technological circuit (author) Nicholas Georgescu-Roegen (media) Energy crisis: Policy response (page) 121 (editor) Peter N. Nemetz
  18. Energy and matter in mankind’s technological circuit (author) Nicholas Georgescu-Roegen (media) Energy crisis: Policy response (page) 121 (editor) Peter N. Nemetz
  19. Analytical economics: issues and problems (page) 73 (author) Nicholas Georgescu-Roegen
  20. Analytical economics: issues and problems (page) 75 (author) Nicholas Georgescu-Roegen
  21. Energy and matter in mankind’s technological circuit (author) Nicholas Georgescu-Roegen (media) Energy crisis: Policy response (page) 120 (editor) Peter N. Nemetz
  22. Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie (media) Abhandlungen Über Die Mechanische Wärmetheorie 2 (date) 1867 (page) 33 (author) Rudolf Clausius
  23. The Entropy Law and the Economic Process (page) 20 (author) Nicholas Georgescu-Roegen
  24. The entropy law and the economic problem (author) Nicholas Georgescu-Roegen (media) Valuing the Earth: Economics, Ecology, Ethics (page) 83 (editor) Herman E. Daly, Kenneth N. Townsend
  25. A young source for the Hawaiian plume (author) Alexander V. Sobolev, Albrecht W. Hofmann, Klaus Peter Jochum, Dmitry V. Kuzmin, Brigitte Stoll