ⓘ Maximum power principle. The maximum power principle or Lotkas principle has been proposed as the fourth principle of energetics in open system thermodynamics, ..

Maximum power principle

ⓘ Maximum power principle

The maximum power principle or Lotkas principle has been proposed as the fourth principle of energetics in open system thermodynamics, where an example of an open system is a biological cell. According to Howard T. Odum, "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."


1. 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 1922a, b. Lotkas statement sought to explain the Darwinian notion of evolution with reference to a physical principle. Lotkas work was subsequently developed by the systems ecologist Howard T. Odum in collaboration with the Chemical Engineer Richard C. Pinkerton, and later advanced by the Engineer Myron Tribus.

While Lotkas work may have been a first attempt to formalise evolutionary thought in mathematical terms, it followed similar observations made by Leibniz and Volterra and Ludwig Boltzmann, 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 Odums 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, itself associated with net energy and EROEI, 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.


2. 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 1978, p. 101 suggested that Odums 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 Odums new law had not yet been validated Gilliland 1978, p. 101. Gilliland stated that in maximum power theory the second law efficiency 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. Perhaps H.T.Odums most concise statement of this view was 1970, p. 62:

The Odum–Pinkerton approach to Lotkas proposal was to apply Ohms law – and the associated maximum power theorem a result in electrical power systems – to ecological systems. 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. 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.


3. 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.

.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.

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


4. Definition in words

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, Odums statement of the maximum power principle relies on the notion of matching, such that high-quality energy maximizes power by matching and amplifying energy: "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.


4.1. Definition in words Mathematical definition

The mathematical definition given by H.T. Odum is formally analogous to the definition provided on the maximum power theorem article. For a brief explanation of Odums approach to the relationship between ecology and electronics see Ecological Analog of Ohms Law


5. 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, Lotkas principle is clarified by stating it as the principle of self organization for maximum empower.

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.

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