Dissipative structure

Example of dissipative structures: granulation on the solar surface. Image diameter approx. 35,000 km

A dissipative structure (engl. Dissipative structure , dissipating structure ') refers to the phenomenon of self-organizing, dynamic, ordered structures in non-linear systems far from the thermodynamic equilibrium . Dissipative structures only form in open non-equilibrium systems that exchange energy , matter, or both with their environment. When creating ordered structures, the entropy decreases locally; this reduction in entropy in the system must be compensated for by an appropriate exchange with the environment.

The development of ordered structures depends crucially on the system parameters, with the transition from the disordered to the ordered state taking place abruptly. Dissipative structures show a certain stability ( non-equilibrium stability ) with respect to external disturbances, but disintegrate as soon as the exchange with the environment is interrupted or generally in the event of major disturbances of the system parameters.

history

As early as 1950 Alan Turing was working on a new mathematical theory of morphogenesis , which shows the effects of non-linear chemical reaction and diffusion functions on spontaneous structure formation. He published the results of this work in 1952 under the title The chemical basis of morphogenesis . This work ( Turing mechanism ) is regarded as groundbreaking for the later discovery of dissipative structures.

The term "dissipative structure" itself was proposed in 1967 by the physical chemist Ilya Prigogine , who was involved in the development of the theory of non-equilibrium thermodynamics from the 1940s . With Grégoire Nicolis and later with R. Lefever, Prigogine investigated the kinetics of open systems that were kept far from thermodynamic equilibrium by the throughput of energy and matter. Based on the work of Alan Turing and Lars Onsager , he showed that in open systems in which autocatalytic chemical reactions take place, inhomogeneities initially occur near thermodynamic equilibrium, which can be maintained by diffusion or flow processes. When reaching a transition point far from equilibrium, the system can show symmetry breaks by forming a stationary, orderly dissipative structure.

Ilya Prigogine received the Nobel Prize in Chemistry in 1977 for his contribution to irreversible thermodynamics, in particular to the theory of "dissipative structures" .

" We have dealt with the fundamental conceptual problems that arise from the macroscopic and microscopic aspects of the second law of thermodynamics. It is shown that non-equilibrium may become a source of order and that irreversible processes may lead to a new type of dynamic states of matter called "dissipative structures". "

- Ilya Prigogine : Nobel Prize Speech 1977.

Thermodynamic description

When building ordered structures, the entropy decreases locally, which is only possible (or likely) in open systems. The change in entropy in a time interval

${\displaystyle \,dS=dS_{i}+dS_{e}}$

divides into an inner ( ) and an outer ( , exchange with the environment) part. In closed systems is no exchange place ( ) and after the second law is always (zero in equilibrium), ie . In open systems, on the other hand, entropy can be exchanged with the environment, and ordered, stationary structures (constant in time) can arise, provided (it applies to a stationary state; according to the second law , this also applies here ) ${\displaystyle \,dS_{i}}$ ${\displaystyle \,dS_{e}}$ ${\displaystyle dS=dS_{i}}$ ${\displaystyle dS_{i}\geq 0}$ ${\displaystyle dS\geq 0}$ ${\displaystyle dS=0}$ ${\displaystyle dS_{i}\geq 0}$

${\displaystyle \,dS_{e}=-dS_{i}<0}$ (negative entropy flow).

Examples

Examples of dissipative structures are the formation of honeycomb cell structures in a liquid heated from below ( Bénard effect ) or at phase boundaries in flow processes, flow equilibria in biochemistry , hurricanes , chemical clocks and candle flames . Dissipative structures have a lot in common with biological organisms , which is why living things are usually counted among these.

The earth's surface, including the atmosphere, forms a non-equilibrium energy-converting ( dissipative ) system that absorbs energy through solar radiation and emits it into space through heat radiation. A large number of dissipative structures can form within this system, such as clouds, rivers or hurricanes.

An economy also forms a dissipative system in which the increase in the degree of complexity increases the throughput of energy and the production of entropy . The so-called technical progress in the sense of the Solow residual can thus be explained by an increase in complexity to increase the efficiency of converting primary energy into useful work for the economic production process. Dissipative structures are capital goods (machines) and organizational forms (companies).

Web links

• Prigogine's Nobel Speech (English; PDF file; 461 kB)
• Helmut Dunkhase: Dialogue with nature: On the 80th birthday of Ilya Prigogine, Berlin, July 1997
• H. Joachim Schlichting: From dissipation to dissipative structure (PDF; 1.2 MB) , Praxis der Naturwissenschaften, 49/2 (2000), pp. 12-16

literature

• Stuart Alan Rice: Special volume in memory of Ilya Prigogine . In: Advances in Chemical Physics Vol. 135 Wiley-Interscience , 2007, ISBN 978-0-471-68233-2
• Ilya Prigogine , Isabelle Stengers : Dialogue with nature. New ways of scientific thinking 1981, ISBN 3492025323

Individual evidence

1. ^ Alan Turing - Unfinished Work.
2. ↑ ^{a b} A. M. Turing: The chemical basis of morphogenesis , Phil. Trans. R. Soc. (London) B237 , 37-72 (1952).
3. ^ Alan Mathison Turing, B. Jack Copeland: The essential Turing. seminal writings in computing, logic, philosophy, artificial intelligence, and artificial life, plus the secrets of Enigma. Oxford University Press, USA, 2004, ISBN 978-0198250807
4. ^ Stuart Alan Rice: Special volume in memory of Ilya Prigogine . In: Advances in Chemical Physics Vol. 135 Wiley-Interscience , 2007, ISBN 978-0-471-68233-2 .
5. ^ ^{A b} I. Prigogine and G. Nicolis: On symmetry-breaking instabilities in dissipative systems. J. Chem. Phys. 46 , 3542-3550 (1967).
6. ↑ Werner Ebeling: Chaos - Order - Information. 2nd edition, Harri Deutsch Verlag, Frankfurt am Main, 1991, ISBN 3-8171-1203-3 , p. 22.
7. ^ I. Prigogine and R. Lefever: On symmetry-breaking instabilities in dissipative systems, II. J. Chem. Phys. 48: 1695-1700 (1968).
8. ↑ ^{a b} Ilya Prigogine: Time, Structure and Fluctuations (PDF; 472 kB) Nobel Lecture, December 8, 1977.
9. ^ Nicolis, Prigogine: Self Organization and Nonequilibrium Systems , Wiley 1977, p. 24.
10. ↑ Reiner Kümmel (2011). The Second Law of Economics: Energy, Entropy, and the Origins of Wealth. Springer Science & Business Media.