maximum power principle
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The maximum power principle or Lotka's principle has been proposed as the fourth principle of energetics in open system
thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...
, where an example of an open system is a biological cell. According to
Howard T. Odum Howard Thomas Odum (September 1, 1924 – September 11, 2002), usually cited as H. T. Odum, was an American ecologist. He is known for his pioneering work on ecosystem ecology, and for his provocative proposals for additional laws of thermod ...
, "The maximum power principle can be stated: During self-organization, system designs develop and prevail that maximize power intake, energy transformation, and those uses that reinforce production and efficiency."H.T. Odum 1995, p. 311


History

Chen (2006) has located the origin of the statement of maximum power as a formal principle in a tentative proposal by
Alfred J. Lotka Alfred James Lotka (March 2, 1880 – December 5, 1949) was a US mathematician, physical chemist, and statistician, famous for his work in population dynamics and energetics. An American biophysicist, Lotka is best known for his propos ...
(1922a, b). Lotka's statement sought to explain the Darwinian notion of evolution with reference to a physical principle. Lotka's work was subsequently developed by the systems ecologist
Howard T. Odum Howard Thomas Odum (September 1, 1924 – September 11, 2002), usually cited as H. T. Odum, was an American ecologist. He is known for his pioneering work on ecosystem ecology, and for his provocative proposals for additional laws of thermod ...
in collaboration with the chemical engineer Richard C. Pinkerton, and later advanced by the engineer
Myron Tribus Myron T. Tribus (October 30, 1921 – August 31, 2016) was an American organizational theorist, who was the director of the Center for Advanced Engineering Study at MIT from 1974 to 1986. He was known as leading supporter and interpreter of W. Ed ...
. While Lotka's work may have been a first attempt to formalise evolutionary thought in mathematical terms, it followed similar observations made by
Leibniz Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathema ...
and
Volterra Volterra (; Latin: ''Volaterrae'') is a walled mountaintop town in the Tuscany region of Italy. Its history dates from before the 8th century BC and it has substantial structures from the Etruscan, Roman, and Medieval periods. History Volter ...
and Ludwig
Boltzmann Ludwig Eduard Boltzmann (; 20 February 1844 – 5 September 1906) was an Austrian physicist and philosopher. His greatest achievements were the development of statistical mechanics, and the statistical explanation of the second law of thermodyn ...
, for example, throughout the sometimes controversial history of natural philosophy. In contemporary literature it is most commonly associated with the work of Howard T. Odum. The significance of Odum's approach was given greater support during the 1970s, amid times of oil crisis, where, as Gilliland (1978, pp. 100) observed, there was an emerging need for a new method of analysing the importance and value of energy resources to economic and environmental production. A field known as
energy analysis Life cycle assessment or LCA (also known as life cycle analysis) is a methodology for assessing environmental impacts associated with all the stages of the life cycle of a commercial product, process, or service. For instance, in the case of ...
, itself associated with
net energy Net Energy Gain (NEG) is a concept used in energy economics that refers to the difference between the energy expended to harvest an energy source and the amount of energy gained from that harvest. The net energy gain, which can be expressed in jo ...
and
EROEI In energy economics and ecological energetics, energy return on investment (EROI), also sometimes called energy returned on energy invested (ERoEI), is the ratio of the amount of usable energy (the ''exergy'') delivered from a particular energy re ...
, arose to fulfill this analytic need. However, in energy analysis intractable theoretical and practical difficulties arose when using the energy unit to understand, a) the conversion among concentrated fuel types (or energy types), b) the contribution of labour, and c) the contribution of the environment.


Philosophy and theory

Lotka said (1922b: 151): Gilliland noted that these difficulties in analysis in turn required some new theory to adequately explain the interactions and transactions of these different energies (different concentrations of fuels, labour and environmental forces). Gilliland (Gilliland 1978, p. 101) suggested that Odum's statement of the maximum power principle (H.T.Odum 1978, pp. 54–87) was, perhaps, an adequate expression of the requisite theory: This theory Odum called maximum power theory. In order to formulate maximum power theory Gilliland observed that Odum had added another law (the maximum power principle) to the already well established laws of thermodynamics. In 1978 Gilliland wrote that Odum's new law had not yet been validated (Gilliland 1978, p. 101). Gilliland stated that in maximum power theory the
second law efficiency Exergy efficiency (also known as the second-law efficiency or rational efficiency) computes the effectiveness of a system relative to its performance in reversible conditions. It is defined as the ratio of the thermal efficiency of an actual system ...
of thermodynamics required an additional physical concept: "the concept of second law efficiency under maximum power" (Gilliland 1978, p. 101): In this way the concept of maximum power was being used as a principle to quantitatively describe the selective law of biological
evolution Evolution is change in the heritable characteristics of biological populations over successive generations. These characteristics are the expressions of genes, which are passed on from parent to offspring during reproduction. Variation ...
. Perhaps H.T.Odum's most concise statement of this view was (1970, p. 62): The Odum–Pinkerton approach to Lotka's proposal was to apply
Ohm's law Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equat ...
– and the associated
maximum power theorem In electrical engineering, the maximum power transfer theorem states that, to obtain ''maximum'' external power from a power source with internal resistance, the resistance of the load must equal the resistance of the source as viewed from its o ...
(a result in
electrical power Electric power is the rate at which electrical energy is transferred by an electric circuit. The SI unit of power is the watt, one joule per second. Standard prefixes apply to watts as with other SI units: thousands, millions and billions of ...
systems) – to ecological systems. Odum and Pinkerton defined "power" in electronic terms as the rate of
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking ** Working animal, an animal tr ...
, where Work is understood as a " useful energy transformation". The concept of maximum power can therefore be defined as the ''maximum rate of useful energy transformation''. Hence the underlying philosophy aims to unify the theories and associated laws of electronic and thermodynamic systems with biological systems. This approach presupposed an analogical view which sees the world as an ecological-electronic-economic engine.


Proposals for maximum power principle as 4th thermodynamic law


Definition in words

Odum et al. viewed the
maximum power theorem In electrical engineering, the maximum power transfer theorem states that, to obtain ''maximum'' external power from a power source with internal resistance, the resistance of the load must equal the resistance of the source as viewed from its o ...
as a principle of power-efficiency reciprocity selection with wider application than just electronics. For example, Odum saw it in open systems operating on solar energy, like both photovoltaics and photosynthesis (1963, p. 438). Like the maximum power theorem, Odum's statement of the maximum power principle relies on the notion of 'matching', such that high-quality energy maximizes power by matching and amplifying energy (1994, pp. 262, 541): "in surviving designs a matching of high-quality energy with larger amounts of low-quality energy is likely to occur" (1994, p. 260). As with electronic circuits, the resultant rate of energy transformation will be at a maximum at an intermediate power efficiency. In 2006, T.T. Cai, C.L. Montague and J.S. Davis said that, "The maximum power principle is a potential guide to understanding the patterns and processes of ecosystem development and sustainability. The principle predicts the selective persistence of ecosystem designs that capture a previously untapped energy source." (2006, p. 317). In several texts H.T. Odum gave the
Atwood machine The Atwood machine (or Atwood's machine) was invented in 1784 by the English mathematician George Atwood as a laboratory experiment to verify the mechanical laws of motion with constant acceleration. Atwood's machine is a common classroom demons ...
as a practical example of the 'principle' of maximum power.


Mathematical definition

The mathematical definition given by H.T. Odum is formally analogous to the definition provided on the
maximum power theorem In electrical engineering, the maximum power transfer theorem states that, to obtain ''maximum'' external power from a power source with internal resistance, the resistance of the load must equal the resistance of the source as viewed from its o ...
article. (For a brief explanation of Odum's approach to the relationship between ecology and electronics see Ecological Analog of Ohm's Law)


Contemporary ideas

Whether or not the principle of maximum power efficiency can be considered the fourth law of thermodynamics and the fourth principle of energetics is moot. Nevertheless, H.T. Odum also proposed a corollary of maximum power as the organisational principle of evolution, describing the evolution of
microbiological Microbiology () is the scientific study of microorganisms, those being unicellular (single cell), multicellular (cell colony), or acellular (lacking cells). Microbiology encompasses numerous sub-disciplines including virology, bacteriology, prot ...
systems,
economic systems An economic system, or economic order, is a system of Production (economics), production, resource allocation and Distribution (economics), distribution of goods and services within a society or a given geographic area. It includes the combinati ...
,
planet A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a you ...
ary systems, and
astrophysical Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline said, Astrophysics "seeks to ascertain the nature of the h ...
systems. He called this corollary the
maximum empower Embodied energy is the sum of all the energy required to produce any goods or services, considered as if that energy was incorporated or 'embodied' in the product itself. The concept can be useful in determining the effectiveness of energy-produ ...
principle. This was suggested because, as S.E. Jorgensen, M.T. Brown, H.T. Odum (2004) note, C. Giannantoni may have confused matters when he wrote "The "Maximum Em-Power Principle" (Lotka–Odum) is generally considered the "Fourth Thermodynamic Principle" (mainly) because of its practical validity for a very wide class of physical and biological systems" (C. Giannantoni 2002, § 13, p. 155). Nevertheless, Giannantoni has proposed the Maximum Em-Power Principle as the fourth principle of thermodynamics (Giannantoni 2006). The preceding discussion is incomplete. The "maximum power" was discovered several times independently, in physics and engineering, see: Novikov (1957), El-Wakil (1962), and Curzon and Ahlborn (1975). The incorrectness of this analysis and design evolution conclusions was demonstrated by Gyftopoulos (2002).


See also

*
Maximum power theorem In electrical engineering, the maximum power transfer theorem states that, to obtain ''maximum'' external power from a power source with internal resistance, the resistance of the load must equal the resistance of the source as viewed from its o ...
*
Maximum entropy thermodynamics In physics, maximum entropy thermodynamics (colloquially, ''MaxEnt'' thermodynamics) views equilibrium thermodynamics and statistical mechanics as Inference#Inference and uncertainty, inference processes. More specifically, MaxEnt applies inferen ...
*
Entropy production Entropy production (or generation) is the amount of entropy which is produced in any irreversible processes such as heat and mass transfer processes including motion of bodies, heat exchange, fluid flow, substances expanding or mixing, anelastic d ...
*
Exergy efficiency Exergy efficiency (also known as the second-law efficiency or rational efficiency) computes the effectiveness of a system relative to its performance in reversible conditions. It is defined as the ratio of the thermal efficiency of an actual system ...
*
Energy conversion efficiency Energy conversion efficiency (''η'') is the ratio between the useful output of an energy conversion machine and the input, in energy terms. The input, as well as the useful output may be chemical, electric power, mechanical work, light (radia ...
* Energy rate density *
Exergy In thermodynamics, the exergy of a system is the maximum useful work possible during a process that brings the system into equilibrium with a heat reservoir, reaching maximum entropy. When the surroundings are the reservoir, exergy is the potent ...
* Jeremy England * Free energy *
Emergy Emergy is the amount of energy consumed in direct and indirect transformations to make a product or service. Emergy is a measure of quality differences between different forms of energy. Emergy is an expression of all the energy used in the work pr ...
*
Systems ecology Systems ecology is an interdisciplinary field of ecology, a subset of Earth system science, that takes a holism, holistic approach to the study of ecological systems, especially ecosystems. Systems ecology can be seen as an application of general ...
* Ecological economics


References

* T.T. Cai, C.L. Montague and J.S. Davis (2006) 'The maximum power principle: An empirical investigation', ''Ecological Modelling'', Volume 190, Issues 3–4, Pages 317–335 * G.Q. Chen (2006) 'Scarcity of exergy and ecological evaluation based on embodied exergy', ''Communications in Nonlinear Science and Numerical Simulation'', Volume 11, Issue 4, July, Pages 531–552. * R.Costanza, J.H.Cumberland, H.E.Daly, R.Goodland and R.B.Norgaard (1997) ''An Introduction to Ecological Economics'', CRC Press – St. Lucie Press, First Edition. * F.L.Curzon and B.Ahlborn (1975) 'Efficiency of a Carnot engine at maximum power output', ''Am J Phys'', 43, pp. 22–24. * C.Giannantoni (2002) ''The Maximum Em-Power Principle as the basis for Thermodynamics of Quality'', Servizi Grafici Editoriali, Padova. * C.Giannantoni (2006) Mathematics for generative processes: Living and non-living systems, ''Journal of Computational and Applied Mathematics'', Volume 189, Issue 1–2, Pages 324–340. * M.W.Gilliland ed. (1978) ''Energy Analysis: A New Public Policy Tool'', AAA Selected Symposia Series, Westview Press, Boulder, Colorado. * C.A.S.Hall (1995) ''Maximum Power: The ideas and applications of H.T.Odum'', Colorado University Press. * C.A.S.Hall (2004) 'The continuing importance of maximum power', ''Ecological Modelling'', Volume 178, Issue 1–2, 15, Pages 107–113 * H.W. Jackson (1959) ''Introduction to Electronic Circuits'', Prentice–Hall. * S.E.Jorgensen, M.T.Brown, H.T.Odum (2004) 'Energy hierarchy and transformity in the universe', ''Ecological Modelling'', 178, pp. 17–28 * A.L.Lehninger (1973) Bioenergetics, W.A. Benjamin inc. * A.J.Lotka (1922a)
Contribution to the energetics of evolution
DF Proc Natl Acad Sci, 8: pp. 147–51. * A.J.Lotka (1922b)
Natural selection as a physical principle
DF Proc Natl Acad Sci, 8, pp 151–4. * H.T.Odum (1963) 'Limits of remote ecosystems containing man', ''The American Biology Teacher'', Volume 25, No. 6, pp. 429–443. * H.T.Odum (1970) Energy Values of Water Sources. in 19th Southern Water Resources and Pollution Control Conference. * H.T.Odum (1978) 'Energy Quality and the Environment', in M.W.Gilliland ed. (1978) ''Energy Analysis: A New Public Policy Tool'', AAA Selected Symposia Series, Westview Press, Boulder, Colorado. * H.T.Odum (1994) ''Ecological and General Systems: An Introduction to Systems Ecology'', Colorado University Press. * H.T.Odum (1995) 'Self-Organization and Maximum Empower', in C.A.S.Hall (ed.) ''Maximum Power: The Ideas and Applications of H.T.Odum'', Colorado University Press, Colorado. * H.T.Odum and R.C.Pinkerton (1955) 'Time's speed regulator: The optimum efficiency for maximum output in physical and biological systems ', ''Am. Sci.'', 43 pp. 331–343. * H.T.Odum and M.T.Brown (2007) ''Environment, Power and Society for the Twenty-First Century: The Hierarchy of Energy'', Columbia University Press. * M.Tribus (1961) § 16.11 'Generalized Treatment of Linear Systems Used for Power Production', ''Thermostatics and Thermodynamics'', Van Nostrand, University Series in Basic Engineering, p. 619. *Novikov I. I., (1958). The efficiency of atomic power stations. ''J. Nuclear Energy II'', Vol. 7, pp. 125–128; translated from ''Atomnaya Energia'', Vol. 3, (1957), No. 11, p. 409 *El-Wakil, M. M. (1962) ''Nuclear Power Engineering'', McGraw-Hill, New York, pp. 162–165. *Curzon F. L., Ahlborn B., (1975) Efficiency of a Carnot engine at maximum power, ''American Journal of Physics'', Vol. 43, pp. 22–24. *Gyftopoulos E. P., (2002). On the Curzon-Ahlborn efficiency and its lack of connection to power producing processes, ''Energy Conversion and Management'', Vol. 43, pp. 609–615. {{DEFAULTSORT:Maximum Power Principle Energy Thermodynamics Principles