ProjectsISSS

By Professor Gianfranco Minati

Professor Ilya Prigogine was born in Moscow, Russia, on January 25, 1917 and died in Bruxelles on May 28, 2003. He was awarded the Nobel Prize for Chemistry in 1977 for his contributions to non-equilibrium thermodynamics, particularly the theory of dissipative structures.

He received both his undergraduate and graduate education in Chemistry at the Universite Libre de Bruxelles.

He was Regental Professor and Ashbel Smith Professor of Physics and Chemical Engineering at the University of Texas in Austin.

In 1967, he founded the Center for Statistical Mechanics, later renamed the Ilya Prigogine Center for Studies in Statistical Mechanics and Complex Systems.

From 1959 on, he was the director of the International Solvay Institutes in Brussels, Belgium.

The outstanding merit of Ilya Prigogine�s scientific work was to provide a better understanding of the role of time in the Physical Sciences and in Biology. He contributed significantly to the understanding of irreversible processes, particularly in systems far from equilibrium. The results of his work on dissipative structures have stimulated many scientists throughout the world and may have profound consequences for our understanding of biological systems.

He was President of the International Society for the Systems Sciences (ISSS) in 1988.

Ilya Prigogine was one of the �great founding fathers� of Systemics. A controversial scientist in his lifetime , he is now acknowledged to be one of the giants of our age. One of his many notable contributions to science was the introduction of the theory of thermodynamics of irreversible processes. In the fifties, scientists used to focus on equilibrium, paying little or no attention to irreversible phenomena, then considered essentially transitory.

Prigogine studied this problem in Physical Chemistry. He attributed to irreversible processes a constructive role, in contrast to the classical approach, which saw in them only decay.. This new and better understanding of the role of time in the physical sciences and in Biology opened up vistas of a new understanding of biological systems.

In several very important books, like �From Being to Becoming: Time and Complexity in the Physical Sciences� based on a series of three lectures given at the University of Texas in 1978 (Austin, 3, 5, and 7 April 1978), which were indebted to the collaboration of other very important scientists, like the Greek mathematician Gregoire Nicolis, he introduced some formal models of systemic processes. The most famous is the so-called �brussellator� (because developed in Bruxelles). This is a system of differential equations describing the evolution of particular complex systems, like chemical clocks (Fig. 1).

The interesting feature of this model is that whatever the initial concentrations are, the system settles down into the same periodic variation of concentrations. The common trajectory is called a limit cycle, and its period depends on the values of the rate coefficients (Fig. 2).

The Brusselator consists of the reaction between two reactants, A and B, leading to products C and D, formed through unstable intermediates X and Y modeled by the equations:

where:

- and are to be interpreted as

concentrations of appropriated

chemical substances.;

- are control parameters

of the model;

- is the usual Laplace�s operator:

fig. 1 - Reaction Diffusion Equations

Approaches of this kind have been of great interest to scientists becoming more and more interested in studying processes of emergence. There are different approaches to emergence. One, called intrinsic emergence, is related to the establishment of unexpected reactions by using a specific model. What is unexpected is in the model used by an observer and not deriving from experimental activities. In the phase space it is possible to see the establishment of different kinds of solutions depending on different factors, like the initial conditions (the system may �forget� or �not forget� initial conditions) giving rise to attractors and bifurcations. The brussellator is of great importance in the mathematical study of systemics, in modeling and in the study of non-linear thermodynamics.

Another great contribution directly linked with the previous research interests is the introduction of the so-called dissipative structures. They are systems existing and established only on the basis of a continuous dissipation of matter-energy. The classic example is the whirlpool. As we all know from daily experience, this structure is maintained only thanks to a continuous flux of matter-energy. This approach allowed a new way of considering the relationship with the environment in which dissipative systems leave their shape. As mentioned above, dissipative structures have been of great importance in establishing a physics of living matter. It is possible to imagine the powerfulness of the concept applied to different disciplinary contexts (corporations, for instance).

Mostly, the new concepts and approaches introduced by Prigogine are considered in theoretical physics only, or used metaphorically in systemics.

I take this opportunity to mention another scientist, a giant of our age, who introduced Synergetics in Physics (in short, the science of combined effects), adding to and completing the picture introduced above: Hermann Haken. It is particularly moving for me to mention this contribution of H. Haken a friend of and contributor to the Italian Systems Society, because Synergetics is also waiting in the wings to become an integral part of systemics, and because the academic relations between the two scientists were somewhat strained.

The best way to honor the deceased Prigogine and the living Haken is to understand the profound systemic importance of their studies and of their differences in the tradition of interdisciplinarity.

ISSS should use the enormous stock of knowledge now available to systemics.

One may speak of a case of �inter-disciplinarity� when one discipline is able to represent by using its own �idiom�, i.e., language the problems, descriptions, models and solutions of another (e.g., the term equilibrium as used in Physics, Psychology, Economics, Biology, and Music).

In commemorating Ilya Prigogine, we also express our gratitude for the humanist interdisciplinarity of many other past Presidents of ISSS who �took all knowledge to be their province�.

      Some of the books published by Ilya Prigogine are:

1998, Modern Thermodynamics: From Heat Engines to Dissipative Structures (with D. Kondepudi) John Wiley & Sons, Chichester

1997, The End of Certainty, Time, Chaos and the New Laws of Nature (with I. Stengers) The Free Press, New York

1989, Exploring Complexity (with G. Nicolis) W. H. Freeman & Co., San Francisco

1983, Order Out of Chaos (with I. Stengers) Bantam Books, New York

1980, From Being to Becoming: Time and Complexity in the Physical Sciences W. H. Freeman & Co., San Francisco

1977, Self-Organization in Non-Equilibrium Systems: From Dissipative Structures to Order Through Fluctuations (with G. Nicolis) J. Wiley & Sons, New York

1962, Nonequilibrium Statistical Mechanics Wiley-Interscience, New York

Prof. Gianfranco Minati http://www.geocities.com/lminati/gminati/index.html ,

President of the Italian Systems Society www.airs.it

July 2003

Editor�s note:

This contribution is based on a presentation Professor Minati gave in the

Plenary in Memoriam of Past Presidents of ISSS

The Forty-seventh Meeting of the ISSS - International Society for the System Sciences July 7th - 11th, 2003 Iraklion, Crete, Greece