Maximum power principle - AbsoluteAstronomy.com

The maximum power principle has been proposed as the fourth principle of energetics in open system thermodynamics

Thermodynamics

Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

, where an example of an open system is a biological cell. According to Howard T. Odum

Howard T. Odum

Howard Thomas Odum was an American ecologist...

(H.T.Odum 1995, p.311), "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."

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 J. Lotka

Alfred James Lotka was a US mathematician, physical chemist, and statistician, famous for his work in population dynamics and energetics. An American biophysicist best known for his proposal of the predator-prey model, developed simultaneously but independently of Vito Volterra...

(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

Systems ecology

Systems ecology is an interdisciplinary field of ecology, taking a holistic approach to the study of ecological systems, especially ecosystems. Systems ecology can be seen as an application of general systems theory to ecology. Central to the systems ecology approach is the idea that an ecosystem...

Howard T. Odum in collaboration with the Chemical Engineer Richard C. Pinkerton, and later advanced by the Engineer Myron Tribus

Myron Tribus

Myron T. Tribus was the director of the Center for Advanced Engineering Study at MIT. He headed the center when it published W. Edwards Deming's book, Out of the Crisis, and became a leading supporter and interpreter of W. Edwards Deming...

.

While Lotka's work may have been a first attempt to formalise evolutionary thought in mathematical terms, it followed similar observations made by Leibniz and Volterra

Vito Volterra

Vito Volterra was an Italian mathematician and physicist, known for his contributions to mathematical biology and integral equations....

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 Odum's approach was given greater support during the 1970s, amid times of oil crisis

1973 oil crisis

The 1973 oil crisis started in October 1973, when the members of Organization of Arab Petroleum Exporting Countries or the OAPEC proclaimed an oil embargo. This was "in response to the U.S. decision to re-supply the Israeli military" during the Yom Kippur war. It lasted until March 1974. With the...

, 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

EROEI

In physics, energy economics and ecological energetics, energy returned on energy invested ; or energy return on investment , is the ratio of the amount of usable energy acquired from a particular energy resource to the amount of energy expended to obtain that energy resource...

, 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 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

Evolution is any change across successive generations in the heritable characteristics of biological populations. Evolutionary processes give rise to diversity at every level of biological organisation, including species, individual organisms and molecules such as DNA and proteins.Life on Earth...

. 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

Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points...

– and the associated maximum power theorem

Maximum power theorem

In electrical engineering, the maximum power transfer theorem states that, to obtain maximum external power from a source with a finite internal resistance, the resistance of the load must be equal to the resistance of the source as viewed from the output terminals...

(a result in electrical power

Electric power

Electric power is the rate at which electric energy is transferred by an electric circuit. The SI unit of power is the watt.-Circuits:Electric power, like mechanical power, is represented by the letter P in electrical equations...

systems) – to ecological systems. Odum and Pinkerton defined "power" in electronic terms as the rate of work

Work (thermodynamics)

In thermodynamics, work performed by a system is the energy transferred to another system that is measured by the external generalized mechanical constraints on the system. As such, thermodynamic work is a generalization of the concept of mechanical work in mechanics. Thermodynamic work encompasses...

, where Work is understood as a "useful energy

Thermodynamic free energy

The thermodynamic free energy is the amount of work that a thermodynamic system can perform. The concept is useful in the thermodynamics of chemical or thermal processes in engineering and science. The free energy is the internal energy of a system less the amount of energy that cannot be used to...

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

Analogical models

Analogical models are a method of representing a phenomenon of the world, often called the ‘target system’ by another, more understandable or analysable system. They are also called dynamical analogies.- Explanation :...

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

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

Atwood machine

The Atwood machine was invented in 1784 by Rev. George Atwood as a laboratory experiment to verify the mechanical laws of motion with constant acceleration...

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

Maximum power theorem

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 systems, economic systems, planetary

Planetary

Planetary means relating to a planet or planets. It can also refer to:* Planetary , a comic book series by Warren Ellis and John Cassaday* Planetary habitability, the measure of an astronomical body's potential to develop and sustain life...

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,
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).

More generally, Bejan and Lorente (2010) showed that all the proposed optimality statements (min, max, opt, and design) have limited ad-hoc applicability, and are unified under the Constructal law of design and evolution in nature.

History

Philosophy and theory

Proposals for maximum power principle as 4th thermodynamic law

Definition in words

Mathematical definition

Contemporary ideas

See also