Order through fluctuations

Since the early 1900s, it has been known that when an ordinary fluid layer is heated from below, a critical point in the heating process is reached (the thermodynamic threshold) beyond which there emerges a macroscopic, hexagonal pattern reminiscent of a honeycomb. This is known as the Be nard instability and represents one of the most easily appreciated examples of a dissipative structure (Glansdorff and Prigogine, 1971). In this situation, initial heating of the horizontal fluid layer from below results only in fluctuations which are rapidly damped but 

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In principle, it is possible to obtain ECC in the absence of molecular orientation if the crystallization is carried out very slowly at high temperatures close to the melting temperature. Thus, Mandelkern obtained polyethylene crystals similar to ECC in their thermodynamic characteristics by a 40 days crystallization of an isotropic melt28. These experiments also characterize one of the possible paths of the generation of order in polymers order through fluctuations 29 (see below). 

In parallel with the studies described above, which concern perfectly deterministic equations of evolution, it appeared necessary to complete the theory by studying the spontaneous fluctuations. Near equilibrium, any deviation is rapidly damped but near a bifurcation point, a fluctuation may may lead the system across the barrier. The fluctuation is then stabilized, or even amplified this is the origin of the phenomenon which Prigogine liked calling creation of order through fluctuations. More specifically, one witnesses in this way a step toward self-organization. 

LS.12. G. Nicolis and I. Prigogine, Self-Organization in Nonequilibrium Systems From Dissipative Structures to Order through Fluctuations, John Wiley Sons [Interscience], New York. Translations in Russian, Japanese, Itahan, and Chinese. 

TNC.47.1. Prigogine, L ordre par fluctuations et le systeme social (Order through fluctuations and the social system), Rhein. Westf. Akad. Wiss., Vortrdge, no. 260, pp. 1-74, 1976. 

GEN.36.1. Prigogine, Order through fluctuation Self-organization and social system, in Evolution and Consciousness, Human Systems in Transition, E. Jantsch and C. Waddington, eds., Addison-Wesley, Reading, MA, 1976, pp. 93-133. 

Nicolis, G. and Prigogine, I. (1977). Self-Organization in Nonequilibrium Systems. From Dissipative Structures to Order Through Fluctuations. Wiley. 

Nicolis, G., Prigogine, I. Selforganization in nonequilibrium systems from dissipative structures to order through fluctuations. John Wiley Sons, New York, 1977. 

Dissipative Structure to Order Through Fluctuations, Wiley-Interscience, New York... 

From Dissipative Structures to Order through Fluctuations. Wiley, New York. Nissler, K., R. Kessler, W. Schellenberger E. Hofmann. 1977. Binding of fructose-6-phosphate to phosphofructokineuse from yeast. Biochem. Biophys. Res. Commun. 79 973-8. 

The threshold between order and chaos seems to be an essential requisite of complex adaptive self-organising systems (order at the edge of chaos). As these systems are dissipative, an order through fluctuations is effective in working between the above mentioned conditions. 

The two concepts of dissipative structures and order through fluctuations encapsulate the main aspects of nonequilibrium order that we describe in this chapter. 

Biochemistry s hidden asymmetry was discovered by Louis Pasteur in 1857. Nearly 150 years later, its true origin remains an unsolved problem, but we can see how such a state might be realized in the framework of dissipative structures. First, we note that such an asymmetry can arise only under far-from-equilibrium conditions at equilibrium the concentrations of the two enantiomers will be equal. The maintenance of this asymmetry requires constant catalytic production of the preferred enantiomer in the face of interconversion between enantiomers, called racemization. (Racemization drives the system to the equilibrium state in which the concentrations of the two enantiomers will become equal.) Second, following the paradigm of order through fluctuations, we will presently see how, in systems with appropriate chiral autocatalysis, the thermodynamic branch, which contains equal amounts of L- and D-enantiomers, can become unstable. The instability is accompanied by the bifurcation of asymmetric states, or states of broken symmetry, in which one enantiomer dominates. Driven by random fluctuations, the system makes, a transition to one of the two possible states. 

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