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Thermoeconomics
Beyond the Second Law

Peter A. Corning, Ph.D.
Institute for the Study of Complex Systems
119 Bryant Street, Suite 212
Palo Alto, CA 94301 USA

Phone: (650) 325-5717
Fax: (650) 325-3775
Email: ISCS@aol.com

Proceedings, 44th Annual Meeting
International Society for the Systems Sciences,
Toronto, Canada, July 16-22, 2000





INTRODUCTION

The Second Law of Thermodynamics is one of the pillars of the physical sciences, and rightly so. It has withstood the test of time, including innumerable, often ingenious efforts to find exceptions or dispute its hegemony. In the life sciences, unfortunately, the Second Law has had a more checkered history. The fact that energy plays a central role in living systems, and in evolution, has long been appreciated. The so-called "power of life" was a centerpiece of Jean Baptiste de Lamarck's evolutionary theory. In the 19th century, Herbert Spencer echoed this theme is his own grandiose "law of evolution." In the early years of the 20th century, physicists Ludwig Boltzmann and Alfred Lotka both defined evolutionary progress in energetic terms. But it was physicist Ervin Schrödinger, in his legendary book What is Life? (1945) who catalyzed the modern approach to thermodynamics and evolution. Schrödinger characterized living systems as being, quintessentially, embodiments of thermodynamic order -- what he called "negative entropy." Whereas the Second Law posits a general tendency toward energy dissipation and maximum disorder in nature (entropy), Schrödinger asserted that living systems are able to elude this dynamic by "extracting" order from their environments. He also spoke of "sucking orderliness" from the natural world.

One problem with this formulation is that Schrödinger conflated energetic order and physical order, though he was not the first to do so. Although it is often assumed that organisms feed upon energy, Schrödinger declared, this is "absurd...What an organism feeds upon is negative entropy" (1945:72).1 The source of this conflation traces to the development of statistical mechanics at the end of the 19th century. As originally formulated by Rudolph Clausius, the Second Law was strictly phenomenological; thermodynamic order referred only to the ability of energy to do work. Therefore, "entropy" was a measure of the dissipation of energy, or its unavailability to do work. In the latter part of the 29th century, however, physicists Ludwig Boltzmann (1909) and Willard Gibbs (1906) reformulated the Second Law in micro-level statistical terms, that is, in terms of the behavior of the constituent atoms in a defined volume, say of gas molecules, with a specific heat content. Gibbs clearly understood that these statistical measures were "entropy analogues," but many other theorists since, including Schrödinger, have assumed that energetic order and physical order are equivalent. Yet this is not necessarily so. There are thought experiments that can be used to illustrate the point that physical order and energetic order need not be isomorphic (see Corning and Kline 1998a).

Among the pernicious effects of this conflation of physical and energetic order has been the mostly unchallenged assumption over the past 50 years or so that a living system can be reduced to a manifestation of thermodynamic (read physical) order that can be defined in purely statistical terms. In Ilya Prigogine's paradigm, for instance, energy inputs are said to create "dissipative structures" that, over time, will evolve toward greater physical order and complexity via a series of instabilities and bifurcations -- like the Bénard Cells in a pan of heated water. How the transition from energetic order to physical order occurs is not clear. Other theorists have focussed on entropy and negative entropy and have proposed that these state functions somehow serve as directive "forces" or causal agencies that act upon the physical environment in a law-like fashion to direct the course of evolution. These theorists not only conflate energetic and physical order but they erase the all-important distinction between physical order and functional organization -- the very hallmark of living systems. (Again, see Corning and Kline 1998a).


THERMOECONOMICS

We find such formulations to be inadequate and misleading. Contrary to Schrödinger's views, we believe that it more accurate to say that living organisms feed upon available energy to create thermodynamic (energetic) order, as well as structural and functional organization, rather than saying that they feed upon a statistical measure called "order". Furthermore, we believe that energetic order, physical order and biological organization are not equivalent. But most important, we believe that the role of energy in evolution can best be defined and understood in economic terms. By that, we mean that living systems do not merely absorb and order available energy. They must "capture" it and use it (expend it) to build biomass and do work; they must utilize energy for development, maintenance, reproduction and further evolution. To put it baldly, life is a contingent and labor-intensive activity, and the energetic benefits must outweigh the costs (inclusive of entropy) if the system is to survive. Indeed, energetic "profitability" is essential to growth and reproduction.

In short, there is a fundamental difference in "ground-zero" assumptions (so to speak) of thermodynamics and thermoeconomics, which are ultimately incompatible. The thermodynamic premise allows (even invites) externally-driven, deterministic models, with their attendant "laws" of evolution. The thermoeconomic perspective is fundamentally Darwinian, in that it assumes that the "struggle for existence" (in Darwin's pellucid phrase) is a process in which living systems must unfailingly "earn a living" in the "economy of nature." In this paradigm, there is no "order for free." Accordingly, the challenge for each of the two "thermo" schools is to show that their core assumption better represents the reality of the evolutionary context. This issue was discussed in some detail in Corning and Kline (1998b). Here I will provide only a very abbreviated discussion of the thermoeconomics paradigm.


A THOUGHT EXPERIMENT: MAXWELL'S DEMON

One of the most compelling, sources of evidence (albeit inadvertently) in support of the core assumption of thermoeconomics is "Maxwell's Demon." In a famous 19th century "thought experiment," since recounted in innumerable discussions of thermodynamics, physicist James Clerk Maxwell proposed a means by which, supposedly, the Second Law might be violated. Maxwell conjured up a fanciful creature that would be stationed at a wall between two enclosed volumes of gases at equal temperatures. (The term "demon" was actually coined by a contemporary colleague, William Thomson.) The demon would then selectively open and close a microscopic trap door in the wall in such a way as to be able to sort out the mixture of fast and slow gas molecules between the two chambers. In this manner, Maxwell suggested, a temperature differential would be created that could be used to do work, thereby reversing the otherwise irreversible thermodynamic entropy. We suspect that Maxwell never thought his successors would take his demon very seriously, but many have. This is why, in the 1920s, physicist Leo Szilard was impelled to argue, in a professional journal, that the energetic costs associated with the demon's efforts (he focussed on the gathering of "information") would cancel out any gains from the sorting process; the demon had to be part of the thermodynamic accounting. Then, in 1949, Leon Brillouin added the argument that, in order to be able to "see" the molecules, the demon would also need illumination. Following Szilard's lead, Brillouin (1949, 1950) stressed that the "information" required to do the sorting involved an offsetting (entropic) cost.

Many other theorists have made similar arguments since (see especially the papers collected by Leff and Rex, 1990), but the demon refuses to die. For instance, physicist David Layzer (1988) revived the argument with the proposal that the demon might be replaced by "a tiny robot" that would be "programmed" with information about the positions and velocities of all the gas molecules after an "initial moment," so that the trap door could be opened and closed automatically. Of course, Layzer conceded, "such a calculation would need to be based on an immense quantity of data...but that is all right in a thought experiment." No, it is not all right. One cannot arbitrarily set aside the constraints of the real world and then claim to have found a way to violate the Second Law. Layzer's argument fails if the vast energetic cost of designing, building and operating the robot, and of acquiring the necessary information, is included. Furthermore, as shown in Kline (1997), the very notion that it could ever become possible to track and sort individual molecules in a volume of gas is scientifically and technically "wildly unfeasible."

Another problem with Maxwell's paradigm, mostly overlooked, is that the demon would be attempting to derive work from a thermal gradient in a control mass with a fixed energy content (an isolated system). If, for example, the two volumes were hooked up to a heat engine coupled to a means for "recapturing" the energy from the work output, it would violate the Kelvin-Planck dictum which states, in effect, that you cannot create a perpetual motion machine; the output would not be completely reversible. So, Maxwell's classic model, even with the assistance of modern technology, is not a paradigm for progress.

The fundamental problem with the Maxwell's Demon paradigm is that it was not really an experiment in physics (thermodynamics) at all but a surreptitious -- unacknowledged -- experiment in biology. Maxwell himself can be blamed in part for creating this muddle. In the famous and much-quoted passage from his 1871 book, Theory of Heat, in which he introduced his imaginary "being", Maxwell wrote that the Second Law is true (quote): "as long as we can deal with bodies only in mass, and have no power of perceiving or handling the separate molecules of which they are made up. But if we conceive a being whose faculties are so sharpened that he can follow every molecule in its course, such a being...would be able to do what is at present impossible to us" (quoted in Leff and Rex 1990:4). Setting aside the egregious implication that such a perceptual feat -- tracking every molecule in a volume of gas -- might ever become feasible,2 Maxwell then proceeded to make a serious conceptual error. He claimed that his hypothetical creature could "without the expenditure of work" create an energetic differential in a divided "vessel". That assertion effectively removed the demon at a stroke from the realm of realism. Of course, Maxwell was only using his metaphor as an illustration of the fact that "statistical methods" are important to micro-level thermodynamic analyses. He did not pose it as a serious theoretical problem.  Unfortunately, many of his successors have taken it seriously; Leff and Rex (1990) provide an annotated bibliography with some 250 references, many of which are concerned either with exorcising or resurrecting the demon.

Beginning with Leo Szilard's famous 1929 paper, Maxwell's thought experiment was redefined in such a way that it forced physicists to include the costs of the demon, especially the informational costs, in the thermodynamic bookkeeping, rather than treating them as "externalities".3 This in itself was a major contribution, whatever may have been the ultimate flaws in Szilard's argument (see Corning and Kline 1998a, Appendix A). As an increasing degree of realism was introduced into the debate, along with various doomed attempts to add technological improvements to the molecular demon (it remains scientifically and technically unfeasible), the physics community ultimately converted the demon experiment into a problem in information theory and, lately, into a pedagogical tool in introductory physics courses.


A CYANOBACTERIUM IN SUNLIGHT

The ultimate failure of physicists to design a "feasible" Maxwell's Demon highlights the fundamental problem associated with defining the evolutionary process in purely thermodynamic terms. Maxwell's Demon shows us, inadvertently, why it cannot be done. In a nutshell, there is no way to operate the demon at a profit. Despite the claims of some physicists and biophysicists, the evolution of living systems can best be "explained" not in terms of the laws of physics (or the concepts of entropy and negentropy) but in terms of "bioeconomics". The laws of thermodynamics describe underlying physical conditions and constraints with which bioenergetic and human-made technological systems must cope, but they do not encompass or explain the "informed," purposive actions of cybernetic control systems. In living systems (and, by extension, in human technology), the locus of causation is not confined to the energetics; it is crucially dependent also on the information-based actions of teleonomic (purposeful) physical structures and activities; in order for living systems to function, "purposeful" work must be done to acquire and make use of available energy, which necessarily entails "extraction" or "production" costs and cybernetic control activity. In effect, the structures and mechanisms associated with the capture and utilization of energy for purposive "work" introduce a new set of "bioeconomic" (and control) criteria into thermodynamic processes. This perspective suggests the need for such familiar economic concepts as capital investments, operating costs, efficiency, even amortization (consider, for example, the annual "retooling" by deciduous trees). A good model for the role of energy in living systems is a cyanobacterium in sunlight. Nature has vastly improved on Maxwell's demon by developing a highly efficient available energy capturing system that regularly operates at a profit. It is time to give bacteria the credit they deserve, and to give Maxwell's demon a decent burial.


THE EVOLUTION OF BIOENERGETIC TECHNOLOGIES

The thermoeconomic paradigm can perhaps be illuminated further by reviewing a few highlights in the evolution of bioenergetic "technologies". (Among the many good sources, see especially Morowitz 1968, 1978; and Nicholls and Ferguson 1992.) The earliest bacterial cells were not able to "feed" upon direct inputs from the solar flux. Photosynthesis was evidently preceded by bioenergetic fermentation -- the consumption of energy-rich organic compounds, such a simple sugars, that were formed spontaneously in the prebiotic environment in the presence of solar radiation (Broda 1978; Curtis and Barnes 1989). In effect, the earliest fermenting bacteria obtained a free lunch, using readily available compounds to produce biomass and do work. The problem with this technology was that it was based on exploiting a strictly limited resource in a relatively inefficient manner. For instance, when yeast bacteria are placed in a barrel of sugar solution, they can recover (in the form of ATP) only about 35% of the content during alcoholic fermentation; the rest is "lost" as entropy (mostly waste heat). But more important, as Broda noted, the first energy crisis in evolution was a result of the fact that a growing population of living organisms were exploiting a finite and ultimately shrinking resource base. Without the invention of a means for tapping directly the renewable energy resources of the sun, the evolutionary process might have come to an early end.

The true significance of photosynthesis has nothing to do with entropy or "negentropy" It has to do with the development of a highly sophisticated nanotechnology for exploiting a virtually unlimited energy resource with fantastic profit potential. Even photosynthetic bacteria are able to capture much more available energy than is required for their own immediate maintenance needs. However, anaerobic fermentation is still a relatively inefficient conversion technology, and the ability to exploit atmospheric sources of carbon (CO2) was only marginally more efficient (Lehninger 1971; Harold 1986). Its principal virtue was that it provided access to an abundant source of raw materials.

The next significant technological improvement, based on a further exploitation of the synergy principle, represented a major breakthrough. Primitive eukaryotic protists developed -- or more likely, enveloped -- specialized chloroplasts, each of which (at least in modern land plants) contain several thousand "photosynthetic systems" consisting of a "reaction center" and 250-400 chlorophyll and carotenoid molecules -- perhaps as many as one million "antenna pigments" altogether (Curtis and Barnes 1989). Moreover, each cell may contain 40-50 chloroplasts. In other words, these specialists have energy-capturing capabilities that are many orders of magnitude greater than those of their prokaryote ancestors. A crucial corollary, however, is that the degree of specialization and the increases in productivity achieved by chloroplasts are in turn critically dependent upon a "combination of labor" in which the chloroplasts are supported by a larger collaborative enterprise, including particularly the metabolic functions provided by the mitochondria, along with an array of other life-sustaining activities. The result is an interdependent "system" that is vastly more productive -- one that, among other things, is capable of producing some fifteen times as much available energy (net of entropy) as do prokaryotes (Margulis and Sagan 1995).

The next major step in the energy story is associated with the evolution of metazoa, complex multicellular organisms which developed new ways of exploiting the synergy principle.  Now each cell, with its 40-50 million antenna pigments, became part of a vastly larger enterprise in which many photosynthetic cells combined forces and developed entire energy-capturing surfaces, each square millimeter of which might contain half a million chloroplasts. And this already huge number (perhaps 2.5 x 1012 pigment molecules) in turn can be multiplied by the light-capturing surface-area on a given plant. For a single deciduous tree, the total number of light-capturing molecules might be astronomically large -- perhaps 5 x 1022.

"Free-loading," or predation, may be a relatively low-cost way to obtain available energy, and this alternative energetic strategy too has very ancient roots. Indeed, it is likely that predatory behaviors preceded the positive symbioses that contributed to the evolution of eukaryotes (Margulis 1993). However, a major evolutionary breakthrough occurred when a new class of predators developed the ability to utilize an accumulating biological waste product (oxygen) to bypass the rigors of photosynthesis and extract energy directly from the biomass of autotrophs using oxidative combustion. This represented a significantly more economical biotechnology. Equally important, it freed the so-called heterotrophs from the need to sit in the sun all day and remain connected to an array of solar panels. However, as Fenchel and Finley (1994) point out, the increasingly complex forms of energy capture and metabolism were products of synergistic relationships, not thermodynamic "instabilities", "fluctuations", or "bifurcations".

Finally, various organisms have developed the ability to utilize exogenous energy "subsidies" to enhance their survival-related activities and reduce internal costs -- from solar radiation to tidal currents, alluvial flooding, prevailing winds, even gravity. In humans, needless to say, these subsidies have had a major effect in shaping not only the destiny of the species but the course of evolution itself. For example, modern agricultural practices require about 10 calories of subsidy for every calorie of output (E.P. Odum 1983). However, the total output per agricultural worker has gone up proportionately. An American farmer can raise enough food to support him/herself and 45-50 other people; a New Guinea horticulturalist can support only 4-5 people.

In sum, the thermoeconomic aspect of the overall evolutionary process has had little or nothing at all to do with "dissipative structures" and everything to do with evolved improvements in the ability of living systems to capture and utilize available energy; it is the organized use of available energy in informed structures that constitutes the center ring in the circus of life. Although this important "progressive" trend has involved the development of new bioenergetic processes with increasingly anti-entropic/synergistic consequences, the key to explaining these changes lies in their "economic" advantages, as Lotka (1922) originally suggested. No detailed cost-benefit analysis of this progressive trend has yet been undertaken, to our knowledge, but the expected findings may be self-evident. In fact, this trend supports one of the axioms of evolutionary theory, tracing back to Malthus and echoed by Darwin, which holds that living organisms have an evolved capacity for unchecked multiplication in the absence of various environmental constraints.


THERMOECONOMIC EFFICIENCY AND EVOLUTION

Several distinct thermoeconomic trends can be seen in the overall evolutionary process, many of which involve progressive improvements in the capacity of living organisms to acquire and utilize available energy. One such trend, reflected in the discussion above, relates to the total quantity of energy "throughput" -- the ratio of biomass to energy captured. For instance, Karasov and Diamond (1985) have shown that small mammals can process food up to ten times faster than lizards of similar size with the same or greater extraction efficiencies, due to a greater intestinal surface area. A second trend, identified by Lotka (1922), has involved an increase in the total energy flux of the biosphere. Ecology textbooks refer to this quantity as the "gross primary production" of the biosphere. Indirect evidence of this trend can be found in correlated environmental changes, most notably the reduction in atmospheric carbon dioxide and the increase in atmospheric oxygen (see E.P. Odum 1983).

Energetic efficiency is an important concept in thermoeconomics. But, as Blake (1991) has pointed out, in living systems energetic efficiency is a multi-levelled concept. It can refer to energy capture, chemical conversions, biomechanical work, locomotion/propulsion costs, and so on. Natural selection sometimes maximizes for one or more forms of energetic efficiency but more often there are compromises, for many different reasons. One example concerns the energetic costs of reproduction in various species. The costs vary enormously, and the reasons are always multi-factored and complex (Harvey 1986). Humans provide another example. The cost of transport for a running human (in oxygen consumption per unit body mass per unit distance travelled) is higher than for many other mammals and birds. Yet humans also excel in endurance, a paradox that reflects evolutionary compromises (Carrier 1984).

Improvements in efficiency can be achieved in at least three different ways. One has to do with a decrease in entropy "production", or the degree to which available energy is fully utilized (often called First Law thermodynamic efficiency). As we noted earlier, not all energetic evolution has resulted in increases in this type of efficiency. Photosynthetic plants "waste" a lot of energy in evapotranspiration, and animals at the top of the food chain are often "wasteful" of available energy when there is no externally-imposed need to "economize". Likewise, human technologies are notoriously wasteful. For example, it requires two joules of energy from coal to produce one joule of electrical power, and automobiles have maximum energetic efficiencies in the neighborhood of 35-40%. Overall, only about 50% of the exogenous energy inputs for human technology is used productively.

Second Law thermodynamic efficiency, on the other hand, refers to the fraction of available energy that is retained, so to speak, in the "outputs" of an energetic process. Thus, to use an example provided by Ayres and Nair (1984), a space heater may operate at 70% First Law efficiency, meaning that only 30% of the available energy goes up the chimney, whereas its Second Law efficiency may be only 4% -- that is, only a small fraction of the heat is turned into mechanical work while the rest is dissipated.

However, the natural world also provides many examples of a third type of energetic efficiency, namely, adaptations to minimize the quantity of energy used in meeting various biological needs. These adaptations range from shelter-building to hibernation, heat-sharing, nest-sharing, physiological adaptations (fur, feathers, subcutaneous fat layers, etc.) and many more. For instance, Le Maho (1977) documented that the huddling behavior of emperor penguins during the long antarctic winter reduces individual energy expenditures by 20-50 percent. Also, it is important to note that one organism's waste may become another's food supply; the many decomposers and scavengers that utilize otherwise wasted energy, or the continuous recycling of oxygen and CO2 between aerobic heterotrophs and photosynthetic organisms, require us to do our energy bookkeeping at the ecosystem level as well as at lower levels in the biosphere. In any case, the explanation for these phenomena is functional (economic) not thermodynamic.

Another form of energetic efficiency has to do with productivity or energetic "profitability" -- the ratio of work output per unit of energy input. It is likely that increased profitability was another general trend in the evolutionary process. This can be inferred from the improvements in energy-capturing technologies described above. Again, these improvements were a result of the workings of natural selection and not the laws of thermodynamics.

Another clear-cut trend, although evolutionists remain uncertain about many of the details, has to do with a long term increase in the earth's total biomass. Wesley (1989), following Ehrenvärd, estimates that there has been a 20-fold increase in biomass from the Cambrian era to the present day. In this regard, we use the concept of "endergy" -- energy stored in various forms, some very temporary and some as permanent as inorganic matter. (Leigh Van Valen, 1976 called it "structural energy," as distinct from what is immediately available for maintenance, growth and reproduction.) Endergy would include not only the biomass tied up in currently living organisms but also the vast quantities of organic detritus contained in fossil fuels -- coal, oil, oil shale, tars -- as well as in limestone, reef corals, petrified wood, and other inorganic products of organic activity. M. King Hubbert (1971) estimated that the total "initial" quantity of coal alone (before human consumption began in earnest) amounted to some 15.28 trillion metric tons (half of which can be commercially mined). And oil reserves have recently been estimated to be equivalent to some 10 trillion barrels (Davis 1990). This represents an enormous accumulation of endergy -- or potentially available energy. (And this says nothing about atomic energy.)


TWO ISSUES IN THE BIOENERGETICS OF EVOLUTION

Two major issues concerning the bioenergetic aspect of evolution should also be briefly mentioned. One is related to a broader issue in evolutionary biology, namely, does natural selection tend to "maximize" for any particular value, or objective? Is there a discoverable trend or general direction to the process? Some theorists have suggested that, in light of its "necessary" role in biological processes, energy-capturing capabilities would likely be a major target of selection. This was first suggested by Lotka (1922, 1945), who formulated a "law" of maximum energy flux. Van Valen (1976) refined this idea further with his so-called "third law of natural selection." Van Valen posited that natural selection would be likely to maximize not for energy flows per se but for what he called "expansive energy" -- i.e., energetic surpluses that would over time enhance the capacity of the biosphere to expand the total quantity of biomass. The progressive improvements in bioenergetic technology that were cited above would seem to lend some support to this hypothesis, and culturally-evolved human technologies have manifestly played a role in human evolution. The major problem with this line of reasoning is that natural selection cannot, over the long run, maximize for any one parameter in a process where there are a large number of important parameters; energetic improvements are unlikely to occur at the expense of other survival criteria.

Finally, there is the vexing issue of "complexity" in evolution. It is generally agreed that there have been significant increases in biological complexity over the course of evolutionary history, but there is also widespread disagreement about how best to measure this complexity and about what it means -- its evolutionary significance.4 Few, if any, Darwinian theorists think that natural selection would maximize for complexity per se; complexity is likely to be an artifact of other functional changes (see Corning 1983, 1995, 1996; Bonner 1988; Maynard Smith and Szathmáry 1995). On the other hand, many anti-Darwinian theorists seem to think that evolution might do just that. We believe that an unbiased reading of the fossil record and the diversity of currently living systems does not support any such hypothesis. Complexity -- thermodynamic or otherwise -- is a contingent survival strategy that is continuously subject to testing and revision in light of fundamentally bioeconomic criteria. From this perspective, it is the functional consequences of various energetic innovations/adaptations that have been responsible for their differential survival and reproduction over the course of evolutionary history. The explanation lies in the economic costs and benefits, not in the laws of physics or in thermodynamic instabilities/fluctuations/bifurcations -- or, for that matter, in the dynamical attractors of chaos theory.


THERMOECONOMICS AND ECONOMICS

A word is in order at this point about the long-standing but uneasy relationship between energetics and the discipline of economics. The roots of this relationship can be traced back to Jean Baptiste de Lamarck, Herbert Spencer, Ludwig Boltzmann and others in the 19th century, who drew attention to the central role of energy capture and utilization in living systems. In this century, the demographer cum physicist Alfred Lotka (1922) was the first to frame the role of energy and evolution within a natural selection context, and he spoke of using an energetic perspective to illuminate the "biophysical foundations of economics." However, it was physical chemist and Nobel Laureate Frederick Soddy who, in the 1920s and 1930s, became the most vigorous proponent of an energy theory of economic value. Soddy wrote: "If we have available energy, we may maintain life and produce every material requisite necessary. That is why the flow of energy should be the primary concern of economics" (1933:56). Meanwhile, a contemporary, Frederick Taylor (the father of "scientific management"), developed a similar but more narrowly conceived labor-energy theory of value that has subsequently been espoused by many theorists. In the post-World War Two era, a number of anthropologists and ecologists embraced energetic theories of cultural evolution, most notably Leslie White (1943, 1949, 1959), Richard Adams (1975), Fred Cottrell (1953, 1972) Eugene Odum (1971) and Howard Odum (1971; Odum and Odum 1982), among others. Yet, as Mirowski (1988) observed, energetic paradigms never really took root in economics until well into the 1970s. What Mirowski calls the "neo-energetics" movement in economics can perhaps be dated to the work of Nicholas Georgescu-Roegen (1971, 1976a,b, 1977a,b, 1979; see also Dragan and Demetrescu 1986) and the growing number of theorists who have attempted to build bridges between economics and thermodynamics over the last two decades. (See especially Hannon 1973; Slesser 1975; Gilliland 1975; Huettner 1976; Berndt 1978; Berry et al., 1978; Costanza 1980; Boulding 1981; Parsons and Harrison 1981; Bryant 1982; Roberts 1982; Ayres and Nair 1984; Proops 1983, 1985, 1987; van Gool and Bruggink 1985; H.T. Odum 1988; Giampietro et al., 1993. A detailed history and critique of energy-economics can be found in Mirowski 1988, 1989.) Unfortunately, these theorists have been ill-served by their sources in the physical sciences.


CONCLUSION

We believe that the entire strategy associated with various attempts to reduce biological evolution and the dynamics of living systems to the principles either of classical, irreversible thermodynamics or to statistical mechanics -- that is to say, to manifestations of simple, one-level physical systems -- is a theoretical cul de sac. Physics is highly relevant to biology, but its explanatory arsenal can deal only with a part of the multi-levelled, multi-faceted causal hierarchy that is found in living systems. We believe that we have outlined a potentially fruitful alternative strategy, one which is capable of shedding new light on the relationship between energy and the evolutionary process. In so doing, we believe that we have also brought this aspect of biological evolution more firmly into a Darwinian framework; we see thermoeconomics as being fully consistent with Darwinian evolutionary principles. Only time will tell whether or not this alternative approach bears fruit.


FOOTNOTES

  1. Schrödinger also failed to provide a way of measuring "negative entropy" phenomenologically.  He defined it mathematically as the reciprocal of Boltzmann's statistical expression for entropy (see Corning and Kline 1998a).


  2. Kline (1997) has shown that, on strictly technical grounds, Maxwell's demon is "wildly unfeasible," for any one of several reasons. (He defines "wildly" as meaning that it is currently beyond our technical capabilities by a factor of more than one million.) The demon would require capabilities for perception/detection, data collection, mechanical operation and feedback control that appear to be totally impracticable, not to mention being totally uneconomic. Kline points out that it is bad science to base theories and thought experiments on events that have no reasonable likelihood of occurring.


  3. Actually, Szilard's influential paper was preceded by a similar line of argument in a thermodynamics textbook by Lewis and Randall in 1923 and by Szilard himself in his 1925 doctoral dissertation at the University of Berlin (see Leff and Rex, 1990).


  4. Kline (1995) has provided an index for measuring the complexity of a system. His "complexity index" (denoted C) is defined in terms of three quantities: "V" for the number of independent variables needed to describe the state of the system, "P" for the number of independent parameters needed to distinguish the system from like systems, and "L" for the number of feedback loops associated with the system (both internal and those that are linked to the system's environment).



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ACKNOWLEDGEMENTS

I am deeply indebted to the late Steve Kline, Woodard Professor of Science, Technology and Society and of Mechanical Engineering, Emeritus, at Stanford University. I benefited greatly from Professor Kline's widely acknowledged expertise in thermodynamics and his patient mentoring. He was also my co-author for a pair of papers on this subject published in Systems Research and Behavioral Science (Corning and Kline 1998a,b). Of course, Prof. Kline is not responsible for any errors in this paper.


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