The Nobel Prize in Chemistry 1977

Ilya Prigogine

Ilya Prigogine (NL) coined the phrase, as a name for the patterns which self-organize in far-from-equilibrium dissipative systems. He thinks they're unbelievably important, and says so at great length in his books. Some of us physicists believe him; some are skeptical; I am leaning towards skepticism.

But to explain. Dissipation inspires the wrath of the moralist and the envy of most others; for the physicist, however, it is merely faintly depressing. We call something dissipative if it looses energy to waste-heat. (Technically: if volume in the phase space is not conserved.) The famous Second Law of Thermodynamics amounts to saying that, if something is isolated from the rest of the world, it will dissipate all the free energy it has. Equivalently, it maximizes its entropy. Thermal equilibrium is the state of maximum entropy.

If something is (in a well-defined sense) near thermal equilibrium, one can show that its behavior is governed by linear differential equations (hence the name "linear thermodynamics" for the appropriate body of theory), and that left to itself it will approach equilibrium exponentially (hence the somewhat more common name "irreversible thermodynamics"). Here we are guided, not by the entropy, but by "entropy production," the rate of increase in entropy. Since, once we reach equilibrium, the entropy cannot increase (by definition), the entropy production at equilibrium is zero, and the entropy production is always decreasing (the "principle of minimum entropy production").

In general, however, things are not well-isolated from the rest of the world. If energy arrives from the outside as quickly as it is dissipated, even bodies in the linear regime can be kept away from equilibrium. (Hence various Creationist arguments about the Second Law are worthless: neither living things nor the Earth are well-isolated from the rest of the universe, as may be observed every day at sunrise.) Thus dissipation, and why dissipative systems are not necessarily dull as dish-water. So you can have structures in dissipative systems, and there's no reason not to call them "dissipative structures", though it's not obvious that there are many interesting generalizations about them.

"Far-from-equilibrium" means that your system is so far from its thermal equilibrium that the linear laws I mentioned a moment ago no longer apply; non-linear terms become important. The only general rule about the solution to non-linear differential equations is that there are no general rules; hence the interest in the subject. (Cf. Chaos and non-linear dynamics.) This is not good news, of course, if what you want to do is extend thermodynamics to the far-from-equilibrium case. But, one might suppose, matters are not totally hopeless; we aren't talking about just any arbitrary system of equations, but the particular ones important in thermodynamics; perhaps there is some general principle (like those of maximum entropy, or minimum entropy production) which can guide us to solutions. What Prigogine claims to have done is to have found, if not another extremum principle, then at least an inequality (a "universal evolution criterion"), and to have used it to work out the theory of dissipative structures, according to which patterns are supposed to form when the uniform, uninteresting "thermodynamic branch" of the system becomes unstable. The math for all this is analogous to that of equilibrium phase transitions with "broken symmetry", where, again, a uniform state becomes unstable, forcing the system into a patterned, coherent one to minimize free energy. Even without Prigogine's claims that this theory is Very Significant to biology and social science, even without the philosophical and cultural importance he claims for it, this would be very interesting, and the big question is whether he's right, i.e., whether and to what the theory applies, whether, so to speak, there are Dissipative Structures and not just dissipative structures.

"Of course he's right," one is tempted to say. "Everyone acknolwedges he's an expert on thermodynamics; he was part of the Brussels School which basically invented irreversible thermodynamics; he won the Nobel Prize, for crying out loud!" But irreversible thermodynamics is very different, and that was a long time ago --- the forties and fifties and early sixties; that was what the Nobel was for. ("And besides the wench is dead.")

And then there is the matter of his scientific peers --- not the systems theorists and similar riff-raff, but the experts in thermodynamics and statistical mechanics and pattern formation. One of them (P. Hohenberg, co-author of the latest Review of Modern Physics book on the state of the art on pattern formation) was willing to be quoted by Scientific American (May 1995, "From Complexity to Perplexity") to the effect that "I don't know of a single phenomenon his theory has explained."

This is extreme, but it becomes more plausible the more one looks into the actual experimental literature. For instance, chemical oscillations and waves are supposed to be particularly good Dissipative Structures; Prigogine and his collaborators have devoted hundreds if not thousands of pages to their analysis, with a special devotion to the Belousov-Zhabotisnky reagent, which is the classic chemical oscillator. Unfortunately, as Arthur Winfree points out (When Time Breaks Down, Princeton UP, 1987, pp. 189--90), "the Belousov-Zhabotinsky reagent ... is perfectly stable in its uniform quiescence," but can be distrubed into oscillation and wave-formation. This is precisely what cannot be true, if the theory of Dissipative Structures is to apply, and Winfree accordingly judges that "the first step [in understanding these phenomena], which no theorist would have anticipated, is to set aside the mathematical literature" produced by a "ponderous industry of theoretical elaboration". --- Needless to say, Winfree is not opposed to theory or mathematics, and his superb The Geometry of Biological Time (Springer-Verlag, 1980) is full of both.

Somewhat more diplomatic is Philip W. Anderson, one of the Old Turks of the Santa Fe Institute, and himself a Nobelist. I refer in particular to the very interesting paper he co-authored with Daniel L. Stein, "Broken Symmetry, Emergent Properties, Disspiative Structures, Life: Are They Related", in F. Eugene Yates (ed.), Self-Organizing Systems: The Emergence of Order (NY: Plenum Press, 1987), p. 445--457. The editor's abstract is as follows: The authors compare symmetry-breaking in thermodynamic equilibrium systems (leading to phase change) and in systems far from equilibrium (leading to dissipative structures). They conclude thgat the only similarity between the two is their ability to lead to the emergent property of spatial variation from a homogeneous background. There is a well-developed theory for the equilbirium case involving the order parameter concept, which leads to a strong correlation of the order parameter over macroscopic distances in the broken symmetry phase (as exists, for example, in a ferromagnetic domain). This correlation endows the structure with a self-scaled stability, rigidity, autonomy or permanence. In contrast, the authors assert that there is no developed thoery of dissipative structures (despite claims to the contrary) and that perhaps there are no stable dissipative structures at all! Symmetry-breaking effects such as vortices and convection cells in fluids --- effects that result from dynamic instability bifurcations --- are considered to be unstable and transitory, rather than stable dissipative structures.

Thus, the authors do not believe that speculation about dissipative structures and their broken symmetries can, at present, be relevant to questions of the origin and persistence of life.

In his memorable series "Etudes sur le temps humain", Georges Poulet devoted one volume to the "Mesure de l'instant".1 There he proposed a classification of authors according to the importance they give to the past, present and future. I believe that in such a typology my position would be an extreme one, as I live mostly in the future. And thus it is not too easy a task to write this autobiographical account, to which I would like to give a personal tone. But the present explains the past. In my Nobel Lecture, I speak much about fluctuations; maybe this is not unrelated to the fact that during my life I felt the efficacy of striking coincidences whose cumulative effects are to be seen in my scientific work.

I was born in Moscow, on the 25th of January, 1917 - a few months before the revolution. My family had a difficult relationship with the new regime, and so we left Russia as early as 1921. For some years (until 1929), we lived as migrants in Germany, before we stayed for good in Belgium. It was at Brussels that I attended secondary school and university. I acquired Belgian nationality in 1949.

My father, Roman Prigogine, who died in 1974, was a chemical engineer from the Moscow Polytechnic. My brother Alexander, who was born four years before me, followed, as I did myself, the curriculum of chemistry at the Université Libre de Bruxelles. I remember how much I hesitated before choosing this direction; as I left the classical (Greco-Latin) section of Ixelles Athenaeum, my interest was more focused on history and archaeology, not to mention music, especially piano. According to my mother, I was able to read musical scores before I read printed words. And, today, my favourite pastime is still piano playing, although my free time for practice is becoming more and more restricted.

Since my adolescence, I have read many philosophical texts, and I still remember the spell "L'évolution créatrice" cast on me. More specifically, I felt that some essential message was embedded, still to be made explicit, in Bergson's remark:

"The more deeply we study the nature of time, the better we understand that duration means invention, creation of forms, continuous elaboration of the absolutely new."

Fortunate coincidences made the choice for my studies at the university. Indeed, they led me to an almost opposite direction, towards chemistry and physics. And so, in 1941, I was conferred my first doctoral degree. Very soon, two of my teachers were to exert an enduring influence on the orientation of my future work.

I would first mention Théophile De Donder (1873-1957).2 What an amiable character he was! Born the son of an elementary school teacher, he began his career in the same way, and was (in 1896) conferred the degree of Doctor of Physical Science, without having ever followed any teaching at the university.

It was only in 1918 - he was then 45 years old - that De Donder could devote his time to superior teaching, after he was for some years appointed as a secondary school teacher. He was then promoted to professor at the Department of Applied Science, and began without delay the writing of a course on theoretical thermodynamics for engineers.

Allow me to give you some more details, as it is with this very circumstance that we have to associate the birth of the Brussels thermodynamics school.

In order to understand fully the originality of De Donder's approach, I have to recall that since the fundamental work by Clausius, the second principle of thermodynamics has been formulated as an inequality: "uncompensated heat" is positive - or, in more recent terms, entropy production is positive. This inequality refers, of course, to phenomena that are irreversible, as are any natural processes. In those times, these latter were poorly understood. They appeared to engineers and physico-chemists as "parasitic" phenomena, which could only hinder something: here the productivity of a process, there the regular growth of a crystal, without presenting any intrinsic interest. So, the usual approach was to limit the study of thermodynamics to the understanding of equilibrium laws, for which entropy production is zero.

This could only make thermodynamics a "thermostatics". In this context, the great merit of De Donder was that he extracted the entropy production out of this "sfumato" when related it in a precise way to the pace of a chemical reaction, through the use of a new function that he was to call "affinity".3

It is difficult today to give an account of the hostility that such an approach was to meet. For example, I remember that towards the end of 1946, at the Brussels IUPAP meeting,4 after a presentation of the thermodynamics of irreversible processes, a specialist of great repute said to me, in substance: "I am surprised that you give more attention to irreversible phenomena, which are essentially transitory, than to the final result of their evolution, equilibrium."

Fortunately, some eminent scientists derogated this negative attitude. I received much support from people such as Edmond Bauer, the successor to Jean Perrin at Paris, and Hendrik Kramers in Leyden.

De Donder, of course, had precursors, especially in the French thermodynamics school of Pierre Duhem. But in the study of chemical thermodynamics, De Donder went further, and he gave a new formulation of the second principle, based on such concepts as affinity and degree of evolution of a reaction, considered as a chemical variable.

Given my interest in the concept of time, it was only natural that my attention was focused on the second principle, as I felt from the start that it would introduce a new, unexpected element into the description of physical world evolution. No doubt it was the same impression illustrious physicists such as Boltzmann5 and Planck6 would have felt before me. A huge part of my scientific career would then be devoted to the elucidation of macroscopic as well as microscopic aspects of the second principle, in order to extend its validity to new situations, and to the other fundamental approaches of theoretical physics, such as classical and quantum dynamics.

Before we consider these points in greater detail, I would like to stress the influence on my scientific development that was exerted by the second of my teachers, Jean Timmermans (1882-1971). He was more an experimentalist, specially interested in the applications of classical thermodynamics to liquid solutions, and in general to complex systems, in accordance with the approach of the great Dutch thermodynamics school of van der Waals and Roozeboom.7

In this way, I was confronted with the precise application of thermodynamical methods, and I could understand their usefulness. In the following years, I devoted much time to the theoretical approach of such problems, which called for the use of thermodynamical methods; I mean the solutions theory, the theory of corresponding states and of isotopic effects in the condensed phase. A collective research with V. Mathot, A. Bellemans and N. Trappeniers has led to the prediction of new effects such as the isotopic demixtion of helium He3+ He4, which matched in a perfect way the results of later research. This part of my work is summed up in a book written in collaboration with V. Mathot and A. Bellemans, The Molecular Theory of Solutions. 8

My work in this field of physical chemistry was always for me a specific pleasure, because the direct link with experimentation allows one to test the intuition of the theoretician. The successes we met provided the confidence which later was much needed in my confrontation with more abstract, complex problems.

Finally, among all those perspectives opened by thermodynamcis, the one which was to keep my interest was the study of irreversible phenomena, which made so manifest the "arrow of time". From the very start, I always attributed to these processes a constructive role, in opposition to the standard approach, which only saw in these phenomena degradation and loss of useful work. Was it the influence of Bergson's "L'évolution créatrice" or the presence in Brussels of a performing school of theoretical biology?9 The fact is that it appeared to me that living things provided us with striking examples of systems which were highly organized and where irreversible phenomena played an essential role.

Such intellectual connections, although rather vague at the beginning, contributed to the elaboration, in 1945, of the theorem of minimum entropy production, applicable to non-equilibrium stationary states.10 This theorem gives a clear explanation of the analogy which related the stability of equilibrium thermodynamical states and the stability of biological systems, such as that expressed in the concept of "homeostasy" proposed by Claude Bernard. This is why, in collaboration with J.M. Wiame,11 I applied this theorem to the discussion of some important problems in theoretical biology, namely to the energetics of embryological evolution. As we better know today, in this domain the theorem can at best give an explanation of some "late" phenomena, but it is remarkable that it continues to interest numerous experimentalists.12

From the very beginning, I knew that the minimum entropy production was valid only for the linear branch of irreversible phenomena, the one to which the famous reciprocity relations of Onsager are applicable.13 And, thus, the question was: What about the stationary states far from equilibrium, for which Onsager relations are not valid, but which are still in the scope of macroscopic description? Linear relations are very good approximations for the study of transport phenomena (thermical conductivity, thermodiffusion, etc.), but are generally not valid for the conditions of chemical kinetics. Indeed, chemical equilibrium is ensured through the compensation of two antagonistic processes, while in chemical kinetics - far from equilibrium, out of the linear branch - one is usually confronted with the opposite situation, where one of the processes is negligible.

Notwithstanding this local character, the linear thermodynamics of irreversible processes had already led to numerous applications, as shown by people such as J. Meixner,14 S.R. de Groot and P. Mazur,15 and, in the area of biology, A. Katchalsky.16 It was for me a supplementary incentive when I had to meet more general situations. Those problems had confronted us for more than twenty years, between 1947 and 1967, until we finally reached the notion of "dissipative structure". 17

Not that the question was intrinsically difficult to handle; just that we did not know how to orientate ourselves. It is perhaps a characteristic of my scientific work that problems mature in a slow way, and then present a sudden evolution, in such a way that an exchange of ideas with my colleagues and collaborators becomes necessary. During this phase of my work, the original and enthusiastic mind of my colleague Paul Glansdorff played a major role.

Our collaboration was to give birth to a general evolution criterion which is of use far from equilibrium in the non-linear branch, out of the validity domain of the minimum entropy production theorem. Stability criteria that resulted were to lead to the discovery of critical states, with branch shifting and possible appearance of new structures. This quite unexpected manifestation of "disorder-order" processes, far from equilibrium, but conforming to the second law of thermodynamics, was to change in depth its traditional interpretation. In addition to classical equilibrium structures, we now face dissipative coherent structures, for sufficient far-from-equilibrium conditions. A complete presentation of this subject can be found in my 1971 book co-authored with Glansdorff.18

In a first, tentative step, we thought mostly of hydrodynamical applications, using our results as tools for numerical computation. Here the help of R. Schechter from the University of Texas at Austin was highly valuable.19 Those questions remain wide open, but our centre of interest has shifted towards chemical dissipative systems, which are more easy to study than convective processes.

All the same, once we formulated the concept of dissipative structure, a new path was open to research and, from this time, our work showed striking acceleration. This was due to the presence of a happy meeting of circumstances; mostly to the presence in our team of a new generation of clever young scientists. I cannot mention here all those people, but I wish to stress the important role played by two of them, R. Lefever and G. Nicolis. It was with them that we were in a position to build up a new kinetical model, which would prove at the same time to be quite simple and very instructive - the "Brusselator", as J. Tyson would call it later - and which would manifest the amazing variety of structures generated through diffusion-reaction processes.20