Glansdorff

Glansdorff P and Prigogine I 1971 Thermodynamio Theory of Structure, Stability and Fluctuations (London Wiley-Interscience)... 

Denbigh, K. G., Thermodynamics of the Steady State, Methuen, London, 1951. Glansdorff, P., and I. Prigogine, Structure, Stability and Fluctuations, John Wiley Sons, New York, 1971. 

This principle is very general, relating neither to the linearity nor to the symmetry of the transport laws. On the other hand, it is difficult to attribute a physical meaning to dxP- The authors later attempted to derive a local potential from this property, and they applied this concept to the study of the chemical and hydrodynamical stability (e.g., the Benard convection). The results of this approach were published in Glansdorff and Prigogine s book Thermodynamic Theory of Structure, Stability and Fluctuations (LS.IO, 10a), published in 1971. 

The year 1967 appears as a crucial year In an important paper by Prigogine and Nicohs, On symmetry-breaking instabilities in dissipative systems (TNC.16), there appears for the first time the term dissipative stmctures. The filiation of this concept with the half-principle of Glansdorff and Prigogine can be clearly perceived in the works of that period (particularly in the paper TNG.17). However, the new approach required a radical change of the theoretical methods. 

LS.IO. P. Glansdorff et I. Prigogine, Structure, Stabilite et Fluctuations, Masson Co., Paris. 

TNC. 10. P. Glansdorff and I. Prigogine, Generalized entropy production and hydrodynamic stability, Phys.Lett. 7, 243-244 (1963). 

TNC. 14.1. Prigogine and P. Glansdorff, Variational properties and fluctuation theory, Physica 31, 1242-1256 (1965). 

TNC.33.1. Prigogine et P. Glansdorff, L ecart a I equilibre interprets comme une source d ordre. Structures dissipatives (The departure from equilibrium interpreted as a source of order), Bull. Cl. Set Acad. Roy. Belg. 59, 673-702 (1973). 

TNC.37. P. Glansdorff, I. Prigogine, and G. Nicolis, The thermodynamic stability theory of nonequilibrium states, Proc. Natl. Acad. Sci. 71, 197-199 (1974). 

TNC.71. P. Glansdorff et 1. Prigogine, Thermodynamique, Dictionnaire encyclopedique Quillet, Suppl. J-Z, pp. 352-356. 

We here have a principle showing that the second law of thermodynamics plays a constmctive role in nonequilibrium systems and thus does not have the need to exceed some threshold in the nonequilibrium constraints as was the case for the Glansdorff-Prigogine dissipative stmctures [67]. The principle of temporal ordering is valid as soon as the system is out of equilibrium and holds arbitrarily far from equilibrium. 

In the course of time open systems that exchange matter and energy with then-environment generally reach a stable steady state. However, as shown by Glansdorff and Prigogine, once the system operates sufficiently far from equilibrium and when its kinetics acquire a nonlinear nature, the steady state may become unstable [15, 18]. Feedback regulatory processes and cooperativity are two major sources of nonlinearity that favor the occurrence of instabilities in biological systems. 

Glansdorff, P. and Prigogine, I. (1971). Thermodynamics of structure, stability and fluctuations. Wiley-Interscience, New York. 

This work is centred around the study of the response to periodic forcing of systems that, when autonomous, had a stable limit cycle surrounding an unstable steady state in their phase plane. For the sake of simplicity—and since many of the fundamental phenomena are the same—we studied two-dimensional systems. We chose two examples of isothermal reactor models the first is an autocatalytic homogeneous Brusselator (Glansdorff and Prigog-ine, 1971) ... 

I want to warmly thank Dr. D. Kondepudi for his kind help in the preparation of this article and for numerous discussions. I also want to thank Prof. P. Glansdorff for a discussion of the historical background of De Donder s work. 

P. Glansdorff, Universite Libre de Bruxelles, Campus Plaine, Bruxelles, Belgium... 

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