Closed systems as described above can generate some degree of order while declining toward equilibrium according to the reaction-diffusion equations. However, if a continuous supply of energy from outside is provided this becomes an open system with some energy dissipated as heat according to the Second Law of Thermodynamics. These systems are described as open dissipative systems and are central to deal with the physics of living organisms.
The term ‘open dissipative system’ was coined by the Russian-born Belgian physical chemist Ilya Prigogine. He was awarded the Nobel Prize in Chemistry in 1977 for his pioneering work his work on ‘dissipative structures’, first published in 1947 as his PhD thesis entitled A Thermodynamic Study of Irreversible Systems1. This work showed that energy flowing in an open dissipative system can produce a local increase in order with a corresponding decrease in entropy, at the expense of its surrounding disorder, ie, increasing entropy around2.
Prigogine developed the Brusselator3, a system of chemicals like the mixture of chemicals used by Belousov, which, as we have seen, generate BZ spatio-temporal patterns as they proceed to equilibrium. In the Brusselator, fresh chemicals are continuously replenished. This results in an ongoing ‘dynamic equilibrium’ that generates chaotic oscillating wave patterns described by the BZ reaction-diffusion rules: a multitude of traveling, concentric and spiral waves develop as long as new reactants are added to the chemical mixture. Prigogine investigated the rules of formation of such order during flow of energy from outside into the open system. He found that the increase in structural complexity, ie order, is associated with a reduction in entropy.
Bottom: The Brusselator in a stable regime that approaches a fixed point.
From: https://en.wikipedia.org/wiki/Brusselator
From: https://en.wikipedia.org/wiki/Brusselator
A similar system, the Oregonator4, was devised by Richard Field and Richard Noyes working at the University of Oregon and is composed of five coupled elementary chemical stoichiometries5. This network is obtained by reduction of the complex chemical mechanism of the BZ reaction, as suggested by Field, Korös and Noyes (1974)6 and referred to as the FKN mechanism.
The reaction-diffusion theory was first proposed by Alan Turing to explain developmental phenomena in biology7. He stated that the initial symmetry in embryos can be broken by the interplay between two diffusible molecules, whose interactions lead to the formation of geometrical patterns. Based on the principle that mutual interactions between a diffusing activator and inhibitor can result in self-organising pattern formation, reaction-diffusion models have provided valuable insights into the mechanisms underlying the emergence of non-linear waves in several biological processes8.
From: https://en.wikipedia.org/wiki/The_Chemical_Basis_of_Morphogenesis
The Earth itself can be regarded as a giant open dissipative system. Energy flowing from the sun and from the Earth’s core generates the rich dynamic structures present on the Earth including the biosphere. The rich chemical nature of the surface of the earth with all its opportunities for interactions has given an enormous potential for the generation of ordered dynamic structures.
- Later published as Ilya Prigogine (1961): Introduction to Thermodynamics of Irreversible Processes, 2nd ed. Interscience ↩︎
- Ilya Prigogine (1997): The End of Certainty – Time, Chaos, and the New Laws of Nature. Simon & Shuster. ↩︎
- The term ‘Brusselator’ is a portmanteau word from ‘Brussels’ (where Prigogine was working) and ‘oscillator’. ↩︎
- The term ‘Oregonator’ is a portmanteau word from ‘Oregon’ (where Field and Noyes were working) and ‘oscillator’. ↩︎
- For more information, see http://www.scholarpedia.org/article/Oregonator ↩︎
- R.J. Field, E. Korös, & R.M. Noyes (1972): Oscillations in chemical systems, Part 2. Thorough analysis of temporal oscillations in the bromate-cerium-malonic acid system, Journal of the American Chemical Society 94, 8649–8664. ↩︎
- Alan Turing (1952): The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences. The Royal Society. 237 (641): 37–72. Click here to download a PDF of the article. ↩︎
- For examples, see Kondo, S. & Miura T. (2010): Reaction-diffusion model as a framework for understanding biological pattern formation. Science 329, 1616–1620.
Murray, J. D. (1988): How the leopard gets its spots. Scientific American 258, 80–87.
Xu, Y., Vest, C. M. & Murray, J. D. (1983): Holographic interferometry used to demonstrate a theory of pattern formation in animal coats. Applied Optics 22, 3479–3483 .
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