Maximum power principle

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The concept of maximum power has been proposed as the fourth principle of energetics and open system thermodynamics. As noted by Chen, this was tentatively proposed first by Alfred J. Lotka (1922a, b). It was subsequently developed further by the systems ecologist Howard T. Odum in collaboration with the Chemical Engineer Richard C. Pinkerton, and later advanced by the Engineer Myron Tribus. It follows similar observations (made by Leibniz and Volterra for example), throughout the history of natural philosophy.

The Odum/Pinkerton approach was to apply Ohm's law - and the associated maximum power theorem (a result in electrical power systems) - to ecological systems. In this way they used the concept of maximum power as a principle which quantitatively describes the law of biological evolution. Odum and Pinkerton defined "power" in electronic terms as the rate of work, 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. This approach presupposed an analogical view which sees the world as an ecological-electronic-economic engine.

Contents 1 Proposals for maximum power principle as 4th thermodynamic law 2 Definition in words 2.1 Mathematical definition 3 Contemporary ideas 4 See also 5 References

[edit] Proposals for maximum power principle as 4th thermodynamic law

It has been pointed out by Boltzmann that the fundamental object of contention in the life-struggle, in the evolution of the organic world, is available energy. In accord with this observation is the principle that, in the struggle for existence, the advantage must go to those organisms whose energy-capturing devices are most efficient in directing available energy into channels favorable to the preservation of the species.

—A.J.Lotka 1922a, p. 147

...it seems to this author appropriate to unite the biological and physical traditions by giving the Darwinian principle of natural selection the citation as the fourth law of thermodynamics, since it is the controlling principle in rate of heat generation and efficiency settings in irreversible biological processes

—H.T.Odum 1963, p. 437

...it may be time to recognize the maximum power principle as the fourth thermodynamic law as suggested by Lotka

—H.T.Odum 1994

[edit] Definition in words

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

Odum et al. viewed the maximum power theorem 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 as a practical example of the 'principle' of maximum power.

[edit] Mathematical definition

The mathematical definition given by H.T.Odum is formally analogous to the definition provided on the maximum power theorem article.

[edit] 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 systems, economic systems, planetary systems, and astrophysical systems. He called this corollary the maximum empower principle. This was suggested because, as S.E.Jorgensen, M.T.Brown, H.T.Odum (2004) note,

Maximum power might be misunderstood to mean giving priority to low level processes. ... However, the higher level transformation processes are just as important as the low level processes. ... Therefore, Lotka's principle is clarified by stating it as the principle of self organization for maximum empower

—p.18

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).

[edit] See also

• Exergy
• Free energy
• Emergy
• Energetics
• Maximum power theorem
• Systems ecology

[edit] 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 (in press) 'Scarcity of exergy and ecological evaluation based on embodied exergy', Communications in Nonlinear Science and Numerical Simulation, p. 16.
• 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 Theromodynamics 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.
• 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.J.Lotka (1922a) 'Contribution to the energetics of evolution' [PDF]. Proc Natl Acad Sci, 8: pp. 147–51.
• A.J.Lotka (1922b) 'Natural selection as a physical principle' [PDF]. 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 (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 amd 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.
• 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.