This paper was written by S. N. Salthe and published in 2010. It is one of the few papers that explains and compares the maximum power principle and the maximum entropy production principle. Salthe makes a number of interesting and important points; for example, he suggests that these principles can explain the development of both abiotic and biotic systems. However, he also argues that the maximum entropy production principle suggests “that most work of dissipative structures is carried out at rates entailing energy flows faster than those that would associate with maximum power.” This conclusion is problematic for a number of reasons.
The abstract states: “I begin with the definition of power, and find that it is finalistic inasmuch as work directs energy dissipation in the interests of some system. The maximum power principle of Lotka and Odum implies an optimal energy efficiency for any work; optima are also finalities. I advance a statement of the maximum entropy production principle, suggesting that most work of dissipative structures is carried out at rates entailing energy flows faster than those that would associate with maximum power. This is finalistic in the sense that the out-of-equilibrium universe, taken as an isolated system, entrains work in the interest of global thermodynamic equilibration. I posit an evolutionary scenario, with a development on earth from abiotic times, when promoting convective energy flows could be viewed as the important function of dissipative structures, to biotic times when the preservation of living dissipative structures was added to the teleology. dissipative structures are required by the equilibrating universe to enhance local energy gradient dissipation.”
Salthe defines the maximum power principle (MPP) as follows: “For any given work load, maximum power is defined as the work rate after which any increase in rate results in less energy efficiency and more entropy production” (p. 116). Below I provide the definitions of the MPP that H. T. Odum has used throughout his career (1). The common thread that runs through them is that the “work rate” and efficiency of energy transformations are both adjusted to maximize the output of useful power.
We can see the difference between Salthe’s definition and Odum’s when we consider the work Odum did with the physicist Richard Pinkerton. Odum and Pinkerton argue that natural selection will tend to maximize the system’s output of useful power and this is done through a trade-off between the speed or rate of energy transformations and their efficiency (1955, p. 332). At the extreme, illustrated through the example of Atwood’s machine, these transformations can be extremely efficient if speed or rate is sacrificed. In this case, the weight that is lifted by Atwood’s machine is slightly less than the weight in the other basket, so the weight lifted moves very slowly. As the weight that is lifted decreases, the speed of the process is increased, its efficiency is decreased and more entropy is produced over time. Odum and Pinkerton do not argue that this increase in the rate or speed of energy transformations is stopped as soon as efficiency is decreased and entropy production increases; they argue that this increase in rate continues until the output of useful power is maximized.
Salthe’s inaccurate definition of the MPP appears to influence his description of the relation between the MPP and the maximum entropy production principle (MEPP). Salthe defines the MEPP as follows: “an energy dissipative system that can assume several to many conformations, will tend too [sic] take up one, or frequently return to one, that maximizes the entropy production from the energy gradients it is dissipating—to a degree consistent with that system’s survival” (p. 117). He goes on to say “energy gradient dissipation can serve as an approximate or rough stand-in for entropy production.” But then he adds, “consequent upon MEPP, if a system produces work, it should tend to work, not at maximum power, but at a greater rate of work production. Effectiveness of work production should trump energy efficiency in most kinds of systems much of the time” (p. 118). This last sentence is consistent with Odum’s definition of the MPP. Salthe does not provide any justifiable reason to think the MEPP will lead systems to produce work at a greater rate of work production than the MPP.
Axel Kleidon, Y. Malhi, and P. M. Cox define the MEPP as follows: “The proposed principle of maximum entropy production (MEPP), based on statistical mechanics and information theory, states that thermodynamic processes far from thermodynamic equilibrium will adapt to steady states at which they dissipate energy and produce entropy at the maximum possible rate.” In this definition of the MEPP, the dissipation of energy and the production of entropy are both maximized.
Salthe’s conclusion that MEPP leads to a “greater rate of work production” than the MPP may also be affected by his use of a unique definition of work: “‘work’ here refers to material adjustments or behaviors made in the interests of some system that continues to persist (at our observational scale). Work is not a typical ‘physical’ variable, as it associates to finality; it is energy utilization for a purpose” (p. 115). In physics, work is not defined in this teleological fashion: work, in physics, is a measure of the “energy transfer that occurs when an object is moved over a distance by an external force at least part of which is applied in the direction of the displacement” (Britannica). In physics, “work” does not need to be for a purpose.
This is not the first time that I have seen a stipulative definition of “work” used to generate a “difference” between the MPP and the MEPP. In my private correspondence with a scientist who has published a considerable amount of work on the MEPP, he suggested that we should use a more specific definition of power and work that refers to work that builds gradients and structures. This more specific definition of power and work, would not refer to processes like radiative transfer or diffusion, which produce entropy without performing “work,” understood in this specific sense. Using these stipulated definitions for power and work, one can then argue that the MEPP is more comprehensive than the MPP because it refers to processes, like radiative transfer and diffusion, which produce entropy without performing work, and the MPP does not.
If, however, we use the standard, non-teleological definitions of power and work used in physics, this alleged difference between the MEPP and the MPP disappears. The process of producing entropy is, itself, viewed as a form of work, and the ability to produce entropy over time is understood as a form of power. This alleged difference between the MEPP and the MPP is merely a semantic issue.
Underlying these semantics issues, there are theoretical reasons the MEPP and the MPP should be understood as measuring two aspects of the same phenomena. The focus on MEPP can tend to overlook a critical issue originally put forth by Lotka, Odum, and Pinkerton: in a Darwinian context, those systems and organisms that are able to dissipate more energy in the processes associated with survival and reproduction have a selective advantage; the entropy produced as this energy is dissipated is selected for, but only incidentally, because of its fundamental relation to the dissipation of energy, which actually drives evolutionary development (Hall and McWhirter, 2023, p. 7). The suggestion that entropy production drives evolutionary development is like suggesting that the vapor trails a plane leaves behind propel it through the air. In this sense, the MEPP provides an effective description of the development of natural systems; however, the maximum power principle provides a better explanation for this development.
We find an explanation for these stipulated, teleological definitions of power and work in Odum’s and Pinkerton’s definition of the MPP in terms of “useful” power. In the example of Atwood’s machine, when the weight differential is extremely high, the weight that is moved will be taken to the top of the system quickly; the weight that does the work, will fall to the ground fast, and much of the energy will be transferred to the ground in the form of heat. The “useful” energy dissipated in this process is the energy that does the work of moving the weight to the top of the system; the energy that is transferred to the ground in the form of heat is not “useful.” The MPP maximizes the output of useful power: this is the power that has an effect on a system’s or organism’s ability to survive and/or reproduce.
Consequently, the entropy production that has a selective advantage in evolutionary processes is associated with the output of “useful” power. This power is going to tend to produce structures: organisms, social systems, economic systems, ecological systems etc. We do not need to use stipulated definitions of power and work to account for this difference between useful and un-useful power, and this difference does give us a reason to doubt that the MEPP and MPP measure two aspects of the same phenomena.
The scientists Leonid Martyushev and Vladimir Seleznev published a paper in 2006 entitled “Maximum Entropy Production Principle in Physics, Chemistry and Biology” (Martyushev and Seleznev, 2006) in which they suggest the discussions of the MEPP have been fragmented and as a result, different research teams have been unaware of the studies performed by other scientists. One of the main objectives of their paper is to overcome this fragmentation. Many of the scientists working on MEPP are even less familiar with the work Lotka and Odum have done on the MPP. Consequently, the relation between these two principles is not well understood. Salthe’s paper takes an important step toward addressing this issue. It should provide a beginning to a long and fruitful dialogue.
S. N. Salthe. 2010. Maximum Power and Maximum Entropy Production: Finalities in Nature. Cosmos and History: The Journal of Natural and Social Philosophy, vol. 6, no. 1.
(1) Over the course of his long career, Odum offered a number of different definitions for the maximum power principle (MPP), which, in some cases, illustrate how the concept has evolved over time. In 1955, Odum and Pinkerton described the MPP as a postulate they made that is based on Lotka’s proposed “law of maximum energy” for biological systems; based on this law they proposed the postulate: “Under the appropriate conditions, maximum power output is the criterion for the survival of many kinds of systems, both living and non-living. In other words, we are taking “survival of the fittest” to mean persistence of those forms which can command the greatest useful energy per unit time (power output)” (1955, p. 332).
In 1971, Odum describes the MPP as a “general energy law” Lotka developed that holds that the “maximization of power for useful purposes was the criterion for natural selection” (1971, p. 32). In 1977, Odum describes the MPP as holding that “the more lasting and hence more probable dynamic patterns of energy flow or power (including the patterns of living systems and civilizations) tend to transform and restore the greatest amount of potential energy at the fastest possible rate” (1977, p. 109). In 1983, Odum describes the MPP as a principle developed by Lotka that suggests that “systems prevail that develop designs that maximize the flow of useful energy” (1983, p. 6). This definition implies that Lotka had defined his principle of maximum energy flux (PMEF) in terms of useful energy. However, this is not the case; Lotka defined it instead in terms of available energy.
In 1995, Odum wrote that the MPP can be stated as follows: “during self-organization, system designs develop and prevail that maximize power intake, energy transformation, and those uses that reinforce production and efficiency” (1995, p. 311). Once again, this definition comes very close to Lotka’s definition of the PMEF. In 2001, Odum describes Lotka suggesting the “maximum power concept as a fundamental energy law rephrased here as follows: “By trial and error many alternatives start to function, but only those designs that contribute more useful energy flow get reinforced and thus selected to continue” (2001, 1361). The use of the term “useful” here distinguishes this definition from that provided by Lotka. In 2007, Odum writes, “systems that prevail are those with loading adjusted to operate at the peak of the power efficiency curve …. During self-organization, these systems reinforce (choose) pathways with optimum load for maximum output” (2007, p. 37). This definition appears to be more in line with that outlined by Odum and Pinkerton in 1955. In a footnote (n. 3), Odum adds, “because every real process requires power, the maximum and most economical collection, transmission, and use of power must be one of the primary selective criteria.” In 2007, Odum described the MEP as an amended version of Lotka’s principle which holds that “self-organization develops designs to maximize empower of each scale at the same time” (2007, p. 89).
Some of these definitions emphasize different aspects of the MPP; some restate the principle in different ways. Taken collectively, they provide a comprehensive picture of what Odum was thinking about when he referred to the MPP.