Theory of dissipative structures

I. Prigogine (Brussels) non-equilibrium thermodynamics, particularly the theory of dissipative structures. 

The flow of matter and energy through an open system allows the system to self-organize, and to transfer entropy to the environment. This is the basis of the theory of dissipative structures, developed by Ilya Prigogine. He noted that self-organization can only occur far away from thermodynamic equilibrium [17]. 

TNC.34.1. Prigogine and R. Lefever, Theory of dissipative structures, Proceedings, Symposium on Synergetics, Schloss Elmau 1972, H. Haken, ed., Teubner, Stuttgart, 1973, pp.l24—135. 

Ilya Prigogine Belgium b. Russia theory of dissipative structures... 

The mathematical theory of dissipative structures is mainly based on approximate methods such as bifurcation theory of singular perturbation theory. Situations like those described in Section VI and that permit an exact solution are rather exceptional. 

Jan. 25,1917, Moscow, Russia - May 28, 2003, Brussels, Belgium) Ilya Prigogine studied chemistry and physics at the Universite Libre de Bruxelles, where he completed his PhD in 1941, and became a professor in 1947. He joined the Brussels -> thermodynamics school founded by Theophile De Donder (1873-1957) and Jean Timmermans (1882-1971). He received the Nobel Prize in Chemistry in 1977 for his contributions to nonequilibrium thermodynamics, particularly the theory of dissipative structure. His work established a thermodynamic basis of -> transport phenomena in electrolyte solutions and -> electrochemical oscillations. 

Within the framework of the theory of dissipative structures, thermodynamic buffering represents a new bioenergetics regulatory principle for the maintenance of a nonequilibrium conditions. Due to the ATP production in oxidative phosphorylation, the phosphate potential is shifted far from equilibrium. Since hydrolysis of ATP drives many processes in the cell, the shift inXp to far from equilibrium results in a shift of all the other potentials into the far from equilibrium regime. 

While Belousov was describing his e)q)eriments into oscillatory chemical reactions, Ilya Prigogine in Brussels was developing theoretical models of nonequilibrium thermodynamics and ended with the notion of "structure dissipative" for which he was awarded the 1977 Nobel Prize in Chemistry. The concept of "Dissipative Structure" is ejq)licitly mentioned in the Nobel quotation "The 1977 Nobel Prize in Chemistry has been awarded to Professor Ilya Prigogine, Brussels, for his contributions to non-equilibrium thermodynamics, particularly the theory of dissipative structures". In the first half of the 1950s, Glansdorff and Balescu defined with Prigogine the thermodynamic criteria necessary for oscillatory behavior in dissipative systems [7]. Nicohs and Lefever then applied these to models of autocatalytic reactions [8]. 

Ilya Prigogine (1917-2003) Belgian physicist and professor at the University Libre de Bruxelles. In 1977, he received the Nobel prize for his contributions to non-equilibrium thermodynamics, particularly the theory of dissipative structures ... 

Prigogine s theory of dissipative structures generated by a combination of nonlinear chemical reactions and diffusion processes (Glansdorff and Prigogine, 1971 Nicolis and... 

Prigogine is best known for extending the second law of thermodynamics to systems that are distant from equilibrium, showing that the formation of dissipative stmctures allows order to emerge from chaos in non-equilibrium systems. These stmctures have since been used to describe not only physical, chemical or biological phenomena, but also the growth of cities or the flow of traffic. Prigogine was awarded the Nobel Prize in Chemistry in 1977 "for his contributions to non-equilibrium thermodynamics, particularly the theory of dissipative structures". 

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