Thermodynamics
Thermodynamics
Thermodynamics
Abstract
During the 19th century physics underwent a revolution. Sadi Carnot, Lord Kelvin, Rudolf Clausius and others founded a new field of physics, thermodynamics, which focuses on the study of energy.
Although energy is one of the most important economic production factors, thermodynamics does not play a key role in Mainstream Economics. However, energy is necessary for every production process and has an impact on nature because it creates environmental damage. Its use leads to irreversible loss of coal, oil and gas. This is the reason why the founder of Ecological Economics Nicholas Georgescu-Roegen focused on thermodynamic considerations in his pioneering work The Entropy Law and the Economic Process (1972).
This concept explains the consequences of the two fundamental laws of thermodynamics: (i) Energy can neither be created nor destroyed, but only transformed. (ii) To give an example of the second law: Heat will by itself always transfer from a hotter to a colder body, like a heated stone will give up its heat to the cooler air surrounding it.
This concept lays the foundation for an understanding that every industrial production process yields joint products, at least one of which is a waste product. This fact is easily communicated to the public, heightening awareness of the danger of our mode of production.
A practical example is the production of steel by using coke and iron ore. The output is not only steel but also the remains of the manufacturing process, such as CO2, waste water, dust etc.
Key Contributers: Stefan Baumgärtner – Werner Böge – Lutz Freytag – Hans-Jürgen Jaksch – Henrike Koschel – Andreas Kuhlmann – Gernhard Maier – Georg Müller-Fürstenberger – Horst Niemes – J.L.R. Proops – Martin Quaas – Gunther Stephan – Gerhard Wagenhals
Related concepts: JOINT PRODUCTION – SUSTAINABILITY & JUSTICE – IRREVERSIBILITY – BASICS OF TIME – EVOLUTION
1. History
Classical mechanics deals with systems with few elements, e.g. a stone falling to the ground or the movement of the planetary system. It is possible to completely describe and know these systems with few measurements. Moreover, all the behaviour of these classical mechanical systems is reversible in time. The laws of quantum mechanics are valid in this kind of world. Temperature and entropy have no place here. We call these systems micro-systems. In contrast, macro-systems, e.g. a pot of water, have many, even often very many, systems. The complexity of these macroscopic systems is very great, e.g. a balloon with one mol of gas contains about 1023 interactive particles; hence it is practically impossible to completely know the state of a macroscopic system. Therefore, it is advisable to restrict oneself to few global observables, such as temperature and pressure, which do not make sense in a micro system. Different physical laws hold for these macro systems. For example, we shall show below that so-called arrows of time – IRREVERSIBILITY – characterise these systems. One variable is of special importance, namely the notion of entropy, unknown until it was discovered by Rudolph Clausius (1822 –1888) in 1865.
The general study of macro systems is the subject of the field of thermodynamics. Its origins lie in the first half of “the 19th century when practitioners, engineers and scientists like James Watt (1736 – 1819), Sadi Carnot (1796 – 1832), James Prescott Joule (1818 –1889), Rudolph Clausius (1822 – 1888) and William Thompson (the later Lord Kelvin, 1824 – 1907) wanted to understand and increase the efficiency of steam at which steam engines, i.e. macro systems, perform useful mechanical work. From the beginning, this endeavour has combined the study of natural systems and the study of engineered systems – created and managed by purposeful human action – in a very particular way, which is rather unusual for a traditional science such as physics” (Baumgärtner 2004: 103).
It was the great economist, the Rumanian Nicolas Georgescu-Roegen (1906 – 1994), who showed in his pioneering study The Entropy Law and the Economic Process (1971: 3) how Thermodynamics can establish the conceptual foundations of Ecological Economics: “The significant fact for the economist is that the new science of thermodynamics began as a physics of economic value and, basically can still be regarded as such. The Entropy Law [i.e. the Second Law of Thermodynamics; the author] itself emerges as the most economic in nature of all natural laws.” This insight led him to demand a radically new beginning of the conceptual foundations of Economics. Georgescu-Roegen is one of the main founders of Ecological Economics.
2. Theory
First, we give a brief overview for the hurried reader (Section 2.1) and only thereafter turn to a general introduction (Section 2.2). To understand the first two Laws of Thermodynamics, it is helpful to know their historical framework (Section 2.3). Since the concept of entropy is so difficult to understand, we offer an additional way to present it. To this end we turn to statistical mechanics (Section 2.4). Entropy was first associated mainly with heat, which happened in phenomenological thermodynamics. The latter’s difference to statistical mechanics is described in Section 2.2. Some indications as to the relationship between entropy and information theory are given in Section 2.6.
2.1 A brief overview for the hurried reader
2.2 Introduction
To get a feeling for the difficulty of understanding Thermodynamics, the following insight from one of the great physicists of the first half of the 20th century Arnold Sommerfeld (1861 – 1951) may be helpful: “Thermodynamics is a curious subject. The first time one engages oneself with it, one does not understand anything of it. The second time one works it over, one thinks one understands everything except for one or two small details. The third time one works through it, one notices that one does not understand anything at all, but in the meantime, one has got so used to it that one does not bother about it anymore” (Wie-sagt-man-noch-Website, last access: 16.10.2018, our translation).
Why do we deal so extensively with such a difficult subject? The reason is that thermodynamics offers new perspectives for the understanding of economic activity and the origins of environmental problems, be it depletion of natural resources or environmental pollution. The two laws of thermodynamics are of utmost importance. By the way, this statement does not hold only for this purpose but also for a much wider context. How important the Second Law of Thermodynamics is was emphasized by one of the greatest physicists of the first half of the 20th century, Arthur S. Eddington (1882 – 1944), the inventor of the light bulb:
“The law that entropy always increases holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations – then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation – well, these experimentalists do bungle things sometimes. But if your theory is found to be against the Second Law of Thermodynamics, I can give you no hope; there is nothing for it but to collapse in deepest humiliation” (Goodreads-Webiste, last access: 16.10.2018). For Ecological Economists it is expedient to notice that the two laws of thermodynamics lead us to recognise that the human economy is an open subsystem embedded in the larger, but finite, system of the natural environment (Boulding 1966, Georgescu-Roegen 1971, Daly 1977, Ayres 1978, Faber et al. 1995 [1983], Baumgärtner et. al. 2006 and many more).
2.3 Historical framework of the First and Second Law of Thermodynamics
How did the central concept of thermodynamics, entropy, and related questions develop since the beginning of the 19th century? “They developed thanks to a fruitful interplay of different disciplines, namely, thermodynamics, analytical mechanics, statistical physics, and communication theory.
The first implicit recognition of the Entropy Law
The First Law of Thermodynamics
Entropy Law of Thermodynamics: the Second Law of Thermodynamics
Analytical formulation of the Second Law of Thermodynamics
Up to the middle of the nineteenth century, the Second Law was still a rather intuitive and therefore vague formulation of empirical facts about energy transformation processes. In 1854, Rudolph Clausius (1822 – 1888) made a decisive step to come to represent it analytically: He formally defined what he termed ‘equivalence value’, later to become ‘entropy’. The inspiration for this idea came from a formal representation of the First Law given by J. Willard Gibbs (1839 – 1903). He knew that energy can neither be created nor destroyed. Yet the energy of a particular sub-system can change. Gibbs realised that infinitely small changes of energy (dU) can formally be represented by a product of some ‘intensive’ variable of the system and an infinitely small change of the corresponding ‘extensive’ variable:
dU = (intensive variable) x (extensive variable).
dU = Σ x dYi with Xi = δU /δYi.
Isolated, closed, and open systems
Isolated systems exchange neither energy nor matter with their surrounding environment.
Closed systems exchange energy, but not matter, with their surrounding environment.
Open systems exchange both energy and matter with their surrounding environment.
Phenomenological thermodynamics
Today there are several branches of thermodynamics, e.g. statistical thermodynamics will be dealt with in the next Section. Up to 1870 only actual phenomena of heat energy were studied and analysed, only at the macroscopic and not on the microscopic level. After 1870 researchers examined atomic and molecular details at the microscopic level, in particular with statistical methods. To distinguish these different approaches, the pre-1870 findings are summarised under the notion of phenomenological thermodynamics, dealing with all the notions, results and interdependencies mentioned above.
Having dealt with the macroscopic level, we now turn to microscopic procedures developed after 1870.
2.4 Attempting to understand the abstract notion of entropy: statistical mechanics
A central, perhaps even the central aspect of the Second Law is that it implies the irreversibility of the evolution of macroscopic systems – IRREVERSIBILITY – EVOLUTION. This circumstance can be seen from empirical observations in everyday experience, e.g. when burning a piece of wood or the birth, living, dying and death of a creature. “Yet the notion of entropy and the Second Law of Thermodynamics still remained rather mysterious. This is owing to the fact that Clausius’ definition of entropy is rather abstract and left entropy as a variable which, at first sight, has nothing to do with irreversibility. Further, phenomenological thermodynamics, with which we have dealt up to now, does not explicitly deal with time. For that reason, temporal irreversibility is hard to grasp in the framework of equilibrium thermodynamics. The relationship between entropy and irreversibility became somewhat clearer, at least as far as the physics of gases was concerned, thanks to Ludwig Boltzmann (1844 – 1906). He gave a mechanical interpretation for entropy which enabled him to explain why it always increases with time (see for extensive explanations Faber et al. 1995: Sections 3.3 and 3.7).
Introducing statistical mechanics
Phenomenological thermodynamics and macroeconomics – statistical mechanics and microeconomics
Explaining the concept of microstates and macrostates
Entropy as a measure of likelihood
where k is Boltzmann’s constant. Entropy has thus become a measure of likelihood: Highly probable macrostates, that is macrostates that can be realised by a large number of microstates, also have high entropy. The irreversibility stated by the Second Law in Claudius’ formulation (in any isolated system entropy always increases or remains constant) now appears as the almost intuitive insight that any given system always evolves from a less probable to a more probable state, where W and S are larger” (Baumgärtner et al. 1995: 7-8; Faber et al. 1995: 100-101).
“Thus, Boltzmann showed that entropy described the degree of order of a system: The lower the entropy, the higher the order; the higher the entropy, the more chaotic the system” (Baumgärtner et al. 1995: 6-8).
2.5 Phenomenological thermodynamics vs. statistical mechanics
2.6 Entropy and information theory
3. The MINE Project: Focus on Fundamental Concepts
3. Practice
It is evident from our presentation above that entropy is a difficult concept to apply. For this reason, we start with a warning (Section 3.1) and then turn to the pioneering way in which Georgescu-Roegen applied the entropy concept to analyse the economic process (Section 3.2). This leads us to the way thermodynamic insights are used in Ecological Economics (Section 3.3). We then offer the notion of joint production – JOINT PRODUCTION – as a relatively easy-to-use and easy-to-understand concept to capture essential thermodynamic constraints (Section 3.4).
3.1 A frequently overlooked warning
The entropy notion is extremely complex. Thus, the Nobel Laureate in Economics Tjalling Koopmans (1910 – 1986) (1973: 13), a physicist by training and whose first two publications were in physics, notes that ‘entropy’ is a more difficult concept than anything economics has to offer.
The physical concept is generally judged to be quite intricate. If we take the word of some specialists, not even all physicists have a perfectly clear understanding of what the concept exactly means. Its technical details are, indeed, overwhelming. And even a dictionary definition suffices to turn one’s intellectual curiosity away. It is therefore no surprise that the application of the entropy concept has given rise not only to many misunderstandings and controversies in Mainstream Economics and Ecological Economics, but often entropy has also been applied incorrectly in social contexts. One reason for this is that one needs a strong background in physics and economics to understand and appreciate the literature on this topic. Here we can only give some indications. For more details we recommend the reader read Baumgärtner et al. (1995) and Faber et al. (2002: chapter 7) which clarifies the use of the entropy concept by surveying the relevant literature. There it is shown which usages are correct and which are mistaken, which application is sensible, and which is not. The survey “act[s] as guide for the newcomer to this field. One of the main messages will turn out to be that understanding the entropy notion is to understand what is possible in Economics and what is not. Thermodynamics can show the outer limits of what is physically and economically possible:
Thus, the restrictions of the way we live in our world will be become more apparent. Further, this quotation contains an important but often overlooked warning: We cannot expect entropy to be of much use in finding explicit solutions to concrete problems. Rather, because of its very general and unifying nature it contributes to the biophysical foundations of economics as large and Ecological Economics in particular. By ‘biophysical’ we mean physical and biological aspects of nature which are relevant for Economics” (Baumgärtner et al. 1995a: 1-2; Faber et al. 2002: 115-116).
3.2 Georgescu-Roegens’s contribution
Nicholas Georgescu-Roegen (hereafter ‘G-R’) (1906-1996) was the first to introduce in his seminal study The Entropy Law and the Economic Process (1971) “the entropy concept into economics in a visionary way. The economic process transforms stocks of highly concentrated and easily available resources – BASICS OF LIFE – (Faber and Manstetten 2010: chapter 8) into products and wastes which contain the same material in lower concentration. For instance, oil, which is found in the earth’s crust in high concentration and in a state of low entropy, serves as fuel, while CO2 is evenly distributed throughout the atmosphere in a state of high entropy. G-R stresses that these economic processes are irreversible in time: The stocks of resources (like oil, coal and ores) are permanently reduced by economic actions. At the same time the stock of wastes from the economic process is permanently increased.
3.3 Thermodynamics as an essential element of Ecological Economics
The application of thermodynamics is presently widely recognised as an essential element in much current ecological-economic thought since it gives rich insights into the nature of economy-environment interactions. The laws of thermodynamics lead us to recognise that the human economy is an open subsystem embedded in the larger, but finite, system of the natural environment (Boulding 1966, Georgescu-Roegen 1971, Daly 1977, Ayres 1978, Faber et al. 1995 [1983], Baumgärtner et.al. 2006 and many more).
Hence, in this view production processes are subject to the laws of thermodynamics” (Baumgärtner et al. 1995: 3-4).
3.4 Joint production as an easy-to-use and easy-to-understand concept – capturing essential thermodynamic constraints
We have mentioned several times above how difficult the notion of entropy is to understand and apply correctly. For over two decades, we have endeavoured to facilitate this understanding. In the phenomenon of joint production – JOINT PRODUCTION –, we found a connection between thermodynamics and economic activity.
In that sense, the concept of joint production can capture the essential thermodynamic constraints on production processes as expressed by the First and Second Laws, through an easy-to-use and easy-to-understand economic concept” (Baumgärtner et al. 1995: 4-5). An extensive description of joint production with an empirical illustration is given in the concept JOINT PRODUCTION.
While thermodynamic considerations belong to the conceptual foundations of Ecological Economics, this is not the case in Mainstream Economics.
4. Literature
Key Literature
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Baumgärtner, S., M. Faber and L.R. Proops (1995) “Entropy: a unifying concept for Ecological Economics”, Discussion Paper No. 226, Department of Economics University of Heidelberg.
Faber, M., R. Manstetten and. L.R. Proops (2002) Ecological Economics. Concepts and Methods, Edward Elgar, Cheltenham, U., Northampton, Ma, USA. [Chapters 6 and 7 of this book deal extensively with thermodynamics].
Faber, M., H. Niemes and G. Stephan (1995/1983), Entropy, Environment and Resources: An Essay in Physico-Economics, 2nd ed. 1995, Berlin, Heidelberg and New York: Springer. English translation by Ingo Pellengahr from: Entropie, Umweltschutz und Rohstoffverbrauch: Eine naturwissenschaftlich ökonomische Untersuchung, Berlin, Heidelberg and New York: Springer, Translated into Chinese in 1990. [One of the first books introducing analytically thermodynamics into Ecological Economics. Chapters 3 and 4 provide an extensive introduction of the notion of entropy for non-physicists].
Georgescu-Roegen, N. (1971) The Entropy Law and the Economic Process. Harvard University Press, Cambridge/Mass. [The classic and unsurpassed monograph on the foundations of Ecological Economics].
Further Reading
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Arrow, K. J. and G. Debreu (1954) “Existence of an equilibrium for a competitive economy”, Econometrica, 22: 265-290.
References
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Thermodynamics
Balian, R. (1991) From Microphysics to Macrophysics I. Springer-Verlag, Berlin Heidelberg, New York. [An excellent overview of the historical development of thermodynamics.]
Boltzmann, L. (1877) Wiener Berichte 76: 373 ff.
Boulding, K.E., (1966) “The Economics of the coming Spaceship Earth”, in H. Jarrett (ed.), Environmental Quality in a Growing Economy, Baltimore and London, John Hopkins University Press: 3-14
Carnot, S. (1824) Réflexion sur la puissance motrice de feu et sur les machines propres à cette puissance. Bachelier, Paris.
Clausius, R. (1854) Fortschritte der Physik 10.[Classical Paper]
Clausius, R. (1865) Annalen der Physik, 125: 353ff. [Classical papers]
Iha, A. (2013) “What is the second law of thermodynamics?”, Guardian, 2013, December 1st https://www.theguardian.com/science/2013/dec/01/what-is-the-second-law-of-thermodynamics. [Good and very short introduction to thermodynamics.]
Kelvin, Lord William Thompson (1852) “On the universal tendency in nature to the dissipation of mechanical energy” Philosophical Magazine 4: 304ff. [A classical paper]
Stumpf, H. and A. Rieckers (1976) Thermodynamik (Thermodynamics), Vols. 1 and 2, Vieweg, Braunschweig.
Ecological Economics
Ayres, R. U., (1978) Resources, Environment, and Economics. Application of Materials/Energy Balance Principle, New York, Wiley.
Baumgärtner, S. (2000): “Thermodynamic of waste generation”. In K. Bisson and J. Proops (editors), Waste in Ecological Economics, Edward Elgar, Cheltenham, UK., and Northampton, MA, USA.
Baumgärtner, S. (2005) “Thermodynamic Models”, in J. Proops and P. Safonov (editors), Modelling in Ecological Economics, Edward Elgar, Cheltenham, UK, Northampton, USA: 102-129.
Baumgärtner, S., M. Faber and L.R. Proops (1995) “Entropy: a unifying concept for Ecological Economics”, Discussion Paper No. 226, Department of Economics University of Heidelberg.
Baumgärtner, S., M. Faber and L.R. Proops (1995a) “The use of the entropy concept I ecological economics”, Discussion Paper No. 227, Department of Economics University of Heidelberg.
Baumgärtner, S., Faber, M. and Schiller, J. (2006), Joint Production and Responsibility. On the Foundation of Environmental Policy, Edward Elgar, Cheltenham. [This book contains the research on joint production carried out in Heidelberg from 1990 to 2006. It is co-authored by ten researchers.]
Baumgärtner, S., Dyckhoff, H., Faber, M., Proops, J.L.R. and Schiller, J., (2001). The Concept of Joint Production and Ecological Economics. Ecological Economics, 36: 365-372. [The short paper is the conceptual basis for the concept Joint Production]
Boulding, K.E., (1966) “The Economics of the coming Spaceship Earth”, in H. Jarrett (ed.), Environmental Quality in a Growing Economy, Baltimore an London, John Hopkins University Press: 3-14. [A pioneering paper on Ecological Economics.]
Daly, H.E. (1977) Steady State Economics: the Economics of Biophysical Equilibrium and Moral Growth, San Francisco, Freeman. [A classic text on Ecological Economics].
Dyke, C. (1988) “Cities as Dissipative Structures”, in W.H. Weber, D.J. Depew and J. D. Smith (eds.).
Eddington, A.S. (1928) The Nature of the Physical World. Cambridge University Press, Cambridge.
Faber, M., F. Jöst, R. Manstetten and G. Müller-Fürstenberger (1996), ‘Kuppelproduktion und Umweltpolitik: Eine Fallstudie zur Chlorchemie und zur Schwefelsäureindustrie’, Journal für praktische Chemie (Chemikerzeitung), 338, 497–505.
Faber, M., R. Manstetten and. L.R. Proops (2002) Ecological Economics. Concepts and Methods, Edward Elgar, Cheltenham, U., Northhampton, Ma, USA. [Chapter 6 of this book deal extensively with thermodynamics].
Faber, M., H. Niemes and G. Stephan (1995/1983), Entropy, Environment and Resources: An Essay in Physico-Economics, 2nd ed. 1995, Berlin, Heidelberg and New York: Springer. English translation by Ingo Pellengahr from: Entropie, Umweltschutz und Rohstoffverbrauch: Eine naturwissenschaftlich ökonomische Untersuchung, Berlin, Heidelberg and New York: Springer, Translated into Chinese in 1990. [One of the firstbooks introducing analytically thermodynamics into Ecological Economics. Chapters 3 and 4 provide an extensive introduction of the notion of entropy for non-physicists.]
Georgescu-Roegen, N. (1971) The Entropy Law and the Economic Process. Harvard University Press, Cambridge/Mass. [The classic and unsurpassed monograph on the foundations of Ecological Economics.]
Georgescu-Roegen, N. (1979) “Energy Analysis and Economic Valuation,” Southern Economic Journal 45: 1023-1058.
Koopmans, T. (1973) “Economics Among the Sciences”. American Economic Revue 69: 1-13.
Proops, J.R (1985) “Thermodynamics and economics: from analogy to physical functioning”, in W. van Gool and J.J.C. Bruggink (eds.), Energy and Time in the Economic and Physical Sciences. North-Holland, Amsterdam.
Information theory
Shannon, C.E (1948) “A mathematical theory of communication”, Bell System Technical Journal 27: 379-423, 623-656. (Reprinted in C.E. Shannon and Weaver, The Mathematical Theory of Communication, University of Illinois Press, Urbana ILL, 1949) [A classic paper on information theory.]
Shannon, C.E, and W. Weaver (1949) The Mathematical Theory of Communication, University of Illinois Press, Urbana ILL. [A standard work on information theory.]
Online-References
Goodreads-Website:
https://www.goodreads.com/quotes/947685-the-law-that-entropy-always-increases-holds-i-think-the (last access: 16.10.2018)Wie-sagt-man-noch-Website:
http://www.wie-sagt-man-noch.de/zitat/18409/thermodynamik+ist+ein+komisches+fach.+das+erste+m.html (last access: 16.10.2018)
Copy Rights
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The content of MINE originates from scientific work published in books and peer-reviewed journals. Quotes are indicated by a special typographic style.
The project team would like to thank the publishers Edward Elgar, Elsevier, Routledge, Springer and Taylor & Francis for granting a reproduction permission.
Furthermore, we want to express our gratitude to Bernd Klauer, Reiner Manstetten, Thomas Petersen and Johannes Schiller for supporting the MINE Project and granting the permission to use parts of the content of their book “Sustainability and the Art of Long-Term Thinking.”
We are indebted to Prof. Joachim Funke, Ombudsman for Good Scientific Practice at Heidelberg University and the legal department at Heidelberg University, for their advice and support.
The main Source of this Concept is:
Faber, M, Niemes, H., G. Stephan (1995/1983) Entropy, Environment and Resources: An Essay in Physico Economics. Springer Verlag, Heidelberg. Reprinted with permission from Springer Nature Customer Centre GmbH (Licence Number: 4474120026267).