(b. Moscow, Russia, 25 January 1917, d. Brussels, Belgium, 28 May 2003), chemistry, irreversible thermodynamics.
Prigogine was awarded the 1977 Nobel Prize “for his contributions to non-equilibrium thermodynamics, particularly the theory of dissipative structures.” His investigations into the origins of irreversibility in nature laid the groundwork for many important advances in nonlinear dynamics and complexity in the second half of the twentieth century.
Early Development Prigogine, whose childhood years were marked by a spatial odyssey across Europe, occasioned by the Russian Revolution, was to spend most of his adult life probing the nature of motion through time. The son of Roman Prigogine, a chemical engineer, and Julia Wichman Prigogine, a conservatory student, the young Prigogine, accompanied by his parents and his older brother Alexander, arrived in Belgium by way of Lithuania and Berlin at the age of twelve and soon became fascinated by history, literature, archaeology, and particularly music. His skills at the keyboard were to provide a source of satisfaction and relaxation throughout his life. After much hesitation, he finally enrolled as an undergraduate in the chemistry curriculum at the Université Libre de Bruxelles, but his wide-ranging intellectual interests, notably in philosophy, continued to influence his scientific trajectory.
Inspired by his mentor at the university, Théophile de Donder, Prigogine became obsessed with understanding the nature of irreversible processes, or what he was later to refer to as “the arrow of time,” a term apparently coined by Arthur Eddington (The Nature of the Physical World, 1929, p. 68). Classical thermodynamics, from the time of Rudolf Julius Emanuel Clausius, focused on the properties of systems at, or at least very near to, equilibrium, where the entropy is a maximum and is therefore constant. Prigogine and de Donder characterized this limited view as “thermostatics,” and noted that in order to comprehend real, as opposed to ideal, natural processes, one has to deal with the entropy-producing phenomena that occur far away from equilibrium and that had been shunned by most physicists, chemists, and engineers as “parasitic,” “transitory” phenomena of marginal importance. In any actual process, Prigogine and de Donder argued, what is significant and interesting is what is changing in time and cannot be undone. In 1945, four years after receiving his doctoral degree from the Université Libre, Prigogine formulated the theorem of minimum entropy production, which describes nonequilibrium stationary states, and noted its significance in relation to the most important far-from-equilibrium systems: living organisms.
Dissipative Structures Prigogine recognized the limitations of his theory of minimum entropy production, particularly for chemical kinetics. Minimum entropy production holds only for the linear branch of irreversible phenomena, that is, for systems not too far from equilibrium, where the Onsager reciprocal relations are valid. In many reacting systems of interest this is not the case, because they are so far from equilibrium that only the forward reaction is relevant; the reverse reaction is negligible. To deal with such systems, Prigogine, with the aid of his colleague Paul Glansdorff, formulated the notion of “dissipative structures,” stable ordered states that can emerge from less ordered states when a system is sufficiently far from equilibrium. By virtue of their distance from equilibrium, these states are able to maintain their order by dissipating energy to the environment. Such states typically develop via fluctuations of increasingly larger magnitude, and fluctuations played a major role in Prigogine’s thinking about temporal evolution. In his Nobel Lecture, he characterized the formation of a dissipative structure in the following terms: “A new supermolecular order appears that corresponds basically to a giant fluctuation stabilized by exchanges of energy with the outside world.”
Although Prigogine and Glansdorff first considered dissipative structures in the context of hydrodynamics, the years during which they developed the approach, 1947 to 1967, saw some remarkable developments in the study of reaction-diffusion systems, and these eventually provided the most important applications of the theory. In 1952 Alan Turing wrote a seminal paper titled “The Chemical Basis of Morphogenesis,” in which he showed that in an appropriate set of chemical reactions whose components diffuse with the proper rates, stable, stationary, spatially periodic structures can arise spontaneously from an initially homogeneous steady state. These dissipative structures, now known as Turing patterns, spawned a cottage industry of theoretical biologists and others in fields from chemistry to geology to economics, who formulated models for pattern formation of various kinds using Turing’s approach and, implicitly, Prigogine’s dissipative structure idea. The existence of Turing patterns was not demonstrated experimentally until 1990, when Patrick De Kepper and collaborators carried out a study of the reaction of chlorite, iodide, and malonic acid in a gel. Nonetheless, in the intervening four decades, scientists were confident of the scientific basis for Turing structures in large measure because of the power of Prigogine’s theory.
A second instance of the application of dissipative structures involves the discovery of oscillating chemical reactions. While it is obvious that any living system contains chemicals whose concentrations increase and decrease periodically, the accidental discovery in 1921 by William Bray of a reaction between hydrogen peroxide and iodide, in which the concentration of iodine undergoes regular increases and decreases, did little to convince a skeptical chemical community that such behavior could occur in a beaker. The vast majority of chemists, perhaps driven by a kind of vitalism, were convinced that the second law of thermodynamics forbade concentration oscillations in a chemical reaction. In fact, the majority of papers written about the Bray reaction until the 1960s are devoted to attempts to discredit Bray’s result. When Boris Belousov serendipitously found a second chemical oscillator in 1958, he was unable to publish his experimental results in a peer-reviewed journal because the referees insisted that his observations contradicted the second law of thermodynamics. Over the following decade, the combination of further experimental work by Anatol Zhabotinsky and the theoretical underpinning provided by the theories of nonequilibrium thermodynamics and dissipative structures convinced the scientific community that the phenomenon was indeed genuine. In the early twenty-first century, the Belousov-Zhabotinsky oscillating reaction serves as the prototype system for a field known as nonlinear chemical kinetics, and the spatiotemporal structures the reaction generates provide insights into a variety of chemical and biological pattern formation phenomena. Prigogine and his student René Lefever also formulated a simple model, now referred to as the Brusselator, which gives rise to a striking wealth of spatial and temporal dissipative structures, including periodic concentration oscillations and Turing patterns.
The Brusselator model consists of four elementary reactions:
A → X
B + X → Y + D
2X + Y → 3X
X → E
where A and B are usually considered to be reactants whose concentrations are maintained constant, and the system is maintained far from equilibrium either by removing D and E as soon as they are produced or by neglecting all reverse reactions. The beauty of this model, whose complexity arises from the trimolecular, autocatalytic third step, is that with the above assumptions it has only two variable concentrations, X and Y, and can therefore be analyzed in great detail using a variety of powerful mathematical tools. The trimolecular step as written is unlikely to arise as a result of simple molecular collisions, but, as Prigogine and his star pupil, Grégoire Nicolis, pointed out, the same kinetics can arise as the result of a sequence of, for example, enzymatic reactions (Nicolis and Prigogine, 1977, p. 94).
Prigogine saw the variety of the universe, and particularly of life, as arising from irreversibility and dissipative structures far from equilibrium. Perhaps in the spirit of Lev Tolstoy’s observation that all happy families resemble one another, while each unhappy family is unhappy in its own way, he wrote, “The laws of equilibrium are universal. However, far from equilibrium the behavior may become very specific. This is of course a welcome circumstance, because it permits us to introduce a distinction in the behavior of physical systems which would be incomprehensible in an equilibrium world” (Frängsmyr, 1993, p. 270). The classical view of irreversible processes is that they increase entropy and hence lead to disorder. The concept of dissipative structures reveals that irreversible processes can, in fact, create order. Irreversible processes make life possible.
Further Contributions Prigogine was a prolific author, not only of research papers, but also of books. His early works were written as textbooks or scientific monographs, focused on such subjects as irreversible thermodynamics and statistical mechanics. He addressed traditional problems in physical chemistry, such as developing theoretical models for liquids, although even as early as 1971 he applied his ideas to more complex, human problems in Kinetic Theory of Vehicular Traffic, written with Robert Herman. The two-fluid theory, adapted from the kinetic theory of gases, which Prigogine and Herman proposed, remains one of the three main approaches to modeling traffic flow.
In 1977 Prigogine and Nicolis wrote their chef d’oeuvre, Self-Organization in Nonequilibrium Systems, in which they laid out how systems could spontaneously self-organize without violating the second law of thermodynamics. The work was important primarily because it created an intellectual framework for understanding how temporal and spatial patterns could arise. Ironically, few scientists have employed Prigogine’s approach to nonequilibrium thermodynamics directly in addressing real systems, but his work provided a solid theoretical foundation that made the study of such systems a respectable scientific enterprise.
As is often the case with major figures in science, in his later years Prigogine turned his attention increasingly to more global questions. In 1986 he published a quasi-popular book with Isabelle Stengers called La Nouvelle alliance, which was published in English as Order Out of Chaos. A more technical work, From Being to Becoming, had appeared in 1980. In these volumes Prigogine sought to come to terms with the question that had vexed him all his life—how can we understand the arrow of time? He was fond of saying, “We do not grow young!” But systems, as he had shown, can do more than decay as they approach equilibrium. He once said to one of the authors of this article, “Rome did not just decline—it also rose.” He had demonstrated that increases in order and complexity do not contradict thermodynamics, as many before him had thought.
What bothered him was that the arrow of time was not to be found in classical theories. The fundamental laws of physics—Newtonian mechanics, Maxwell’s equations of electrodynamics, quantum mechanics—are all time-reversible, meaning that one can substitute –t for t and the equations remain unchanged. If these laws were all that governed nature, the arrow of time would be an illusion, as many scientists, including Einstein, believed. However, consistent with human experience, the phenomenological laws that describe irreversible processes such as heat and mass diffusion do not remain unchanged by a substitution of –t for t. If one puts a drop of red ink into a beaker of water, one ends up with a beaker of pink water; the reverse transition never occurs. In his lectures at the University of Texas at Austin, where he spent three months a year in his Center for Studies in Statistical Mechanics, Prigogine would explain how a movie showing a temperature gradient being spontaneously created (without any chemical reactions) would tell the viewer that the movie was being played backwards. An observer can tell which way the video should be played because there is an intrinsic arrow of time. The arrow of time, Prigogine believed, is as fundamental as the existence of time itself, and he sought to reconcile this idea with the underlying laws of physics, even if it meant turning traditional theories on their head and thinking of mechanics as an approximation in a world that is ultimately irreversible.
In his later years, Prigogine became increasingly concerned with the role of time in quantum mechanics and with the related issue of the interplay between dynamics and thermodynamics. He saw a kind of complementarity between dynamics, based on knowledge of individual trajectories, which are reversible, and thermodynamics, where entropy, which can only increase in time, plays the key role. He argued that the key lay in recasting some of the fundamental equations describing mechanical systems in such a way that key operators, in particular the Liouville operator, are no longer represented by unitary transformations. In this way, the time reversal symmetry is broken, and a single trajectory for a system is no longer an observable. Irreversibility and the second law then emerge in a much more fundamental way. Whether Prigogine’s reformulation of some of the most basic laws of physics will ultimately be accepted as successfully reconciling the apparent inconsistencies between dynamics and thermodynamics remains a matter of some controversy, much as the first expositions of his earlier ideas about the importance of irreversible processes were met with considerable skepticism.
Prigogine’s Milieu Prigogine was a true citizen of the world, and his contributions were recognized time and again. He was a member of more than a dozen national academies and received more than forty honorary degrees. In addition to the 1977 Nobel Prize, he received the Solvay Prize in 1955, the Rumford Gold Medal of the Royal Society in 1976, and the Honda Prize in 1983, along with many other international awards. He was a major figure in the development of an integrated approach to scientific research in Europe during the 1980s, stressing the need to encourage unconventional ideas and approaches, which he referred to as “hopeful fluctuations.” He was keenly interested in the phenomenon of globalization, seeing it as an analog of long distance communication in nonliving systems, about which he wrote, “matter in equilibrium is blind, and it communicates over short distances over a short time. Matter out of equilibrium begins to see” (1989, p. 399). In addition to his professorship at the Université Libre in Brussels, he directed the International Solvay Institutes of Physics and Chemistry from 1959 to 2003 and was a professor in the Physics Department at the University of Texas in Austin, where he spent increasing portions of his time at his Ilya Prigogine Center for Studies in Statistical Mechanics, Thermodynamics and Complex Systems after his mandatory retirement from Brussels in 1987. For many years, his department in Brussels attracted those seeking to understand complex behavior in physical and biological systems, and some of the brightest minds in the world were drawn to the department, both as students and as visitors.
Prigogine’s ideas provided a framework for many of the key developments in late-twentieth-century science, from chaos theory to self-organization, but his views were by no means universally accepted. Perhaps because it challenged some of the most revered figures in science, perhaps because he attempted to apply it so widely (another scientist once condescendingly remarked about the work coming out of Brussels, “A theory of everything is a theory of nothing”), Prigogine’s vision often evoked heated controversy, and he knew it. He once told a prospective postdoctoral student to consider working on a safer topic, because “Research is like horse betting, interesting return is with the outsiders, but there is high risk to lose everything.”
Prigogine and his first wife, Helene Jofé, had a son, Yves, in 1945. His second marriage, to Marina Prokopowicz in 1961, produced a son, Pascal, in 1970. In 1981 he was awarded hereditary nobility and the title of viscount by the king of Belgium. What drove Prigogine throughout his extraordinary life and scientific career is perhaps best summed up in these lines from the poet Kahlil Gibran: “Time has been transformed, and we have changed; it has advanced and set us in motion; it has unveiled its face, inspiring us with bewilderment and exhilaration” (Gibran, The Vision, London: Penguin, 2004, p. 29).
A complete bibliography can be found in Ilya Prigogine's Is Future Given?, cited below.
WORKS BY PRIGOGINE
Structure, Dissipation and Life. Amsterdam: North-Holland, 1969.
With Paul Glansdorff. Thermodynamic Theory of Structure, Stability and Fluctuations. New York: John Wiley and Sons, 1971.
With Grégoire Nicolis. Self-Organization in Nonequilibrium Systems: From Dissipative Structures to Order through Fluctuations. New York: Wiley Interscience, 1977.
Autobiographie. Brussels: Florilège des Sciences en Belgique II, 1980.
From Being to Becoming. San Francisco: W. H. Freeman, 1980. “The Philosophy of Instability.” Futures 21 (1989): 396–400.
With Isabelle Stengers. The End of Certainty—Time, Chaos, and the New Laws of Nature. New York: Free Press, 1997.
With Dilip Kondepudi. Modern Thermodynamics, from Heat Engines to Dissipative Structures. Chichester, U.K.: John Wiley and Sons, 1998.
Is Future Given? River Edge, NJ: World Scientific Press, 2003.
Castets, Vincent, Etienette Dulos, Jacques Boissonade, et al. “Experimental Evidence of a Sustained Standing Turing-Type Nonequilibrium Chemical-Pattern.” Physical Review Letters 64 (1990): 2953–2956.
Frängsmyr, Tore, ed. Nobel Lectures in Chemistry, 1971–1980. Singapore: World Scientific, 1993.
Kovac, Jeffrey. “Ilya Prigogine, 1977 Nobel Laureate.” In Nobel Laureates in Chemistry 1901–1992, edited by Laylin K. James. Washington, DC: American Chemical Society and Chemical Heritage Foundation, 1993.
Turing, Alan M. “The Chemical Basis of Morphogenesis.” Philosophical Transactions of the Royal Society of London Series B-Biological Sciences 237 (1952): 37–72.
Irving R. Epstein
John A. Pojman
PRIGOGINE, Ilya. Belgian (born Russia), b. 1917. Genres: Sciences. Career: University of Brussels, Brussels, Belgium, instructor, 1947-50; professor, 1950-87, professor emeritus of chemistry and physics, 1987-; University of Texas at Austin, director of Ilya Prigogine Center for Studies in Statistical Mechanics, and Complex Systems, 1967-, Ashbel Smith Regental Professor of Physics and Chemical Engineering, 1984-, Chimie, 1959-; visiting professor at University of Chicago, Enrico Fermi Institute for Nuclear Studies, and Institute for the Study of Metals, 1961-66; member of administrative council of Fondation Erasme, 1983; chairman of rector's advisory committee of United Nations University; director of studies at Ecole des Hautes Etudes en Sciences Sociales, 1987; distinguished scientific member of Fondation Max-Planck; member of Haut Conseil de la Franco- phonie; consultant to European Communities Commission; president of UNESCO's Institut Europeen pour la Cooperation Est-Ouest, 1990; Nobel Prize in Chemistry, 1977. Publications: (with R. Defay) Traite de thermodynamique conformement aux methodes de Gibbs et de De Donder, Volume I: Thermodynamique chimique, 1944, Volume II (with Defay, Andre Belle- mans, and P. Everett): Tension superficielle et adsorption, 1951; Etude thermodynamique des phenomenes irreversibles, 1947, trans. as Introduction to Thermodynamics of Irreversible Processes, 1954, 3rd ed. 1967; (with A.Bellemans and V. Mathot) The Molecular Theory of Solutions, 1957; (with R. Herman) Kinetic Theory of Vehicular Traffic, 1971; (with P. Glansdorff) Thermodynamic Theory of Structure, Stability, and Fluctuations, 1971; (with G. Nicolis) Self-Organization in Non-Equilibrium Systems: From Dissipative Structures to Order through Fluctuations, 1977; (with I. Stengers) La Nouvelle Alliance: Les Metamorphoses de la science, 1979, trans. as Order Out of Chaos: Man's New Dialogue with Nature, 1983; From Being to Becoming: Time and Complexity in the Physical Sciences, 1980; (with G. Nicolis) Exploring Complexity, 1989; (with I. Stengers) Entre le temps et l'eternite, 1988; Les Lois de Chaos, 1994; Time, Chaos and the Laws of Chaos, 1994; La Fin des Certitudes, 1996. Died 2003.
PRIGOGINE, ILYA (1917–2003), mathematician and Nobel laureate in chemistry. Born in Moscow, Prigogine moved with his family to Belgium at the age of four. His father was a chemist and Prigonine, who had a lifelong interest in music and history, obtained his doctorate in chemistry in 1947 at the Free University of Brussels, whose staff he then joined. However, his broad intellectual interests profoundly influenced the direction of his scientific research. From 1959 to 2003, he was director of the International Solvay Institutes in Brussels and in 1967 he founded Ilya Prigogine Center for Studies in Mathematics and Complex Systems at the University of Texas at Austin, Texas. When he started his life's work, conventional attitudes were based on the Second Law of Thermodynamics, which states that heat can never pass spontaneously from a colder to a hotter body, with the inference that energy transfer is unidirectional and all natural processes are irreversible. Prigigone and his associates used physical chemical experiments and mathematical modeling to understand the basis of stability in chemical reactions and biological systems. He refined the earlier concept of entropy, a measure of disorder in a system, with the theory of dissipation, that is, the regulated fluctuations which promote stability in the face of irreversible change. His theoretical and mathematical formulation of "dissipative structures" created by irreversible processes led to the award of the Nobel Prize in 1977. In his later years Prigogine became increasingly concerned with applying novel thermodynamic principles to the complexities of human biology and even human behavior. A natural extension of his interests was his concern for the potentially disastrous impact of human activities on the environment.
[Michael Denman (2nd ed.)]