*Translation from the French
text*

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
Boltzmann^{5} and Planck^{6} 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 He^{3}+ He^{4},
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}

This is the place to pay tribute to the pioneering work of the
late A. Turing,^{21} who, since 1952,
had made interesting comments about structure formation as
related to chemical instabilities in the field of biological
morphogenesis. I had met Turing in Manchester about three years
before, at a time when M.G. Evans, who was to die too soon, had
built a group of young scientists, some of whom would achieve
fame. It was only quite a while later that I recalled the
comments by Turing on those questions of stability, as, perhaps
too concerned about linear thermodynamics, I was then not
receptive enough.

Let us go back to the circumstances that favoured the rapid
development of the study of dissipative structures. The attention
of scientists was attracted to coherent non-equilibrium
structures after the discovery of experimental oscillating
chemical reactions such as the Belusov-Zhabotinsky
reaction;^{22} the explanation of its
mechanism by Noyes and his co-workers;^{23} the study of oscillating reactions in
biochemistry (for example the glycolytic cycle, studied by B.
Chance^{24} and B. Hess^{25}) and eventually the important research led by
M. Eigen.^{26} Therefore, since 1967, we have been confronted
with a huge number of papers on this topic, in sharp contrast
with the total absence of interest which prevailed during
previous times.

But the introduction of the concept of dissipative structure was
also to have other unexpected consequences. It was evident from
start that the structures were evolving out of fluctuations. They
appeared in fact as giant fluctuations, stabilized through matter
and energy exchanges with the outer world. Since the formulation
of the minimum entropy production theorem, the study of
non-equilibrium fluctuation had attracted all my
attention.^{27} It was thus only
natural that I resumed this work in order to propose an extension
of the case of far-from-equilibrium chemical reactions.

This subject I proposed to G. Nicolis and A. Babloyantz. We
expected to find for stationary states a Poisson distribution
similar to the one predicted for equilibrium fluctuations by the
celebrated Einstein relations.
Nicolis and Babloyantz developed a detailed analysis of linear
chemical reactions and were able to confirm this
prediction.^{28} They added some
qualitative remarks which suggested the validity of such results
for any chemical reaction.

Considering again the computations for the example of a
non-linear biomolecular reaction, I noticed that this extension
was not valid. A further analysis, where G. Nicolis played a key
role, showed that an unexpected phenomenon appeared while one
considered the fluctuation problem in nonlinear systems far from
equilibrium: the distribution law of fluctuations depends on
their scale, and only "small fluctuations" follow the law
proposed by Einstein.^{29} After a
prudent reception, this result is now widely accepted, and the
theory of non-equilibrium fluctuations is fully developing now,
so as to allow us to expect important results in the following
years. What is already clear today is that a domain such as
chemical kinetics, which was considered conceptually closed, must
be thoroughly rethought, and that a brand-new discipline, dealing
with non-equilibrium phase transitions, is now
appearing.^{30, 31,
32}

Progress in irreversible phenomena theory leads us also to
reconsideration of their insertion into classical and quantum
dynamics. Let us take a new look at the statistical mechanics of
some years ago. From the very beginning of my research, I had had
occasion to use conventional methods of statistical mechanics for
equilibrium situations. Such methods are very useful for the
study of thermodynamical properties of polymer solutions or
isotopes. Here we deal mostly with simple computational problems,
as the conceptual tools of equilibrium statistical mechanics have
been well established since the work of Gibbs and Einstein. My
interest in non-equilibrium would by necessity lead me to the
problem of the foundations of statistical mechanics, and
especially to the microscopic interpretation of
irreversibility.^{33}

Since the time of my first graduation in science, I was an
enthusiastic reader of Boltzmann, whose dynamical vision of
physical becoming was for me a model of intuition and
penetration. Nonetheless, I could not but notice some
unsatisfying aspects. It was clear that Boltzmann introduced
hypotheses foreign to dynamics; under such assumptions, to talk
about a dynamical justification of thermodynamics seemed to me an
excessive conclusion, to say the least. In my opinion, the
identification of entropy with molecular disorder could contain
only one part of the truth if, as I persisted in thinking,
irreversible processes were endowed with this constructive role I
never cease to attribute to them. For another part, the
applications of Boltzmann's methods were restricted to diluted
gases, while I was most interested in condensed systems.

At the end of the forties, great interest was aroused in the
generalization of kinetic theory to dense media. After the
pioneering work by Yvon^{34},
publications of Kirkwodd^{35}, Born and
Green^{36}, and of
Bogoliubov^{37} attracted a lot of
attention to this problem, which was to lead to the birth of
non-equilibrium statistical mechanics. As I could not remain
alien to this movement, I proposed to G. Klein, a disciple of
Fürth who came to work with me, to try the application of
Born and Green's method to a concrete, simple example, in which
the equilibrium approach did not lead to an exact solution. This
was our first tentative step in non-equilibrium statistical
mechanics.^{38} It was eventually a
failure, with the conclusion that Born and Green's formalism did
not lead to a satisfying extension of Boltzmann's method to dense
systems.

But this failure was not a total one, as it led me, during a
later work, to a first question: Was it possible to develop an
"exact" dynamical theory of irreversible phenomena? Everybody
knows that according to the classical point of view,
irreversibility results from supplementary approximations to
fundamental laws of elementary phenomena, which are strictly
reversible. These supplementary approximations allowed Boltzmann
to shift from a dynamical, reversible description to a
probabilistic one, in order to establish his celebrated H
theorem.

We still encountered this negative attitude of "passivity"
imputed to irreversible phenomena, an attitude that I could not
share. If - as I was prepared to think - irreversible phenomena
actually play an active, constructive role, their study could not
be reduced to a description in terms of supplementary
approximations. Moreover, my opinion was that in a good theory a
viscosity coefficient would present as much physical meaning as a
specific heat, and the mean life duration of a particle as much
as its mass.

I felt confirmed in this attitude by the remarkable publications
of Chandrasekhar and von Neumann, which were also issued during
the forties.^{39} That was why, still
with the help of G. Klein, I decided to take a fresh look at an
example already studied by Schrödinger,^{
40} related to the description of a system of harmonic
oscillators. We were surprised to see that, for all such a simple
model allowed us to conclude, this class of systems tend to
equilibrium. But how to generalize this result to non-linear
dynamical systems?

Here the truly historic performance of Léon van Hove opened
for us the way (1955).^{41} I remember,
with a pleasure that is always new, the time - which was too
short - during which van Hove worked with our group. Some of his
works had a lasting effect on the whole development of
statistical physics; I mean not only his study of the deduction
of a "master equation " for anharmonic systems, but also his
fundamental contribution on phase transitions, which was to lead
to the branch of statistical mechanics that deals with so-called
"exact" results.^{42}

This first study by van Hove was restricted to weakly coupled
anharmonic systems. But, anyway, the path was open, and with some
of my colleagues and collaborators, mainly R. Balescu, R. Brout,
F. Hénin and P. Résibois, we achieved a formulation of
non-equilibrium statistical mechanics from a purely dynamical
point of view, without any probabilistic assumption. The method
we used is summed up in my 1962 book.^{43} It leads to a "dynamics of correlations", as
the relation between interaction and correlation constitutes the
essential component of the description. Since then, these methods
have led to numerous applications. Without giving more detail,
here, I will restrict myself to mentioning two recent books, one
by R. Balescu,^{44} the other by P.
Résibois and M. De Leener.^{45}

This concluded the first step of my research in non-equilibrium
statistical mechanics. The second is characterized by a very
strong analogy with the approach of irreversible phenomena which
led us from linear thermodynamics to non-linear thermodynamics.
In this tentative step also, I was prompted by a feeling of
dissatisfaction, as the relation with thermodynamics was not
established by our work in statistical mechanics, nor by any
other method. The theorem of Boltzmann was still as isolated as
ever, and the question of the nature of dynamics systems to which
thermodynamics applies was still without answer.

The problem was by far more wide and more complex than the rather
technical considerations that we had reached. It touched the very
nature of dynamical systems, and the limits of Hamiltonian
description. I would never have dared approach such a subject if
I had not been stimulated by discussions with some highly
competent friends such as the late Léon Rosenfeld from
Copenhagen, or G. Wentzel from Chicago. Rosenfeld did more than
give me advice; he was directly involved in the progressive
elaboration of the concepts we had to explore if we were to build
a new interpretation of irreversibility. More than any other
stage of my scientific career, this one was the result of a
collective effort. I could not possibly have succeeded had it not
been for the help of my colleagues M. de Haan, Cl. George, A.
Grecos, F. Henin, F. Mayné, W. Schieve and M. Theodosopulu.
If irreversibility does not result from supplementary
approximations, it can only be formulated in a theory of
transformations which expresses in "explicit" terms what the
usual formulation of dynamics does "hide". In this perspective,
the kinetic equation of Boltzmann corresponds to a formulation of
dynamics in a new representation.^{46,
47, 48, 49}

In conclusion: dynamics and thermodynamics become two
complementary descriptions of nature, bound by a new theory of
non-unitary transformation. I came so to my present concerns;
and, thus, it is time to end this intellectual autobiography. As
we started from specific problems, such as the thermodynamic
signification of non-equilibrium stationary states, or of
transport phenomena in dense systems, we have been faced, almost
against our will, with problems of great generality and
complexity, which call for reconsideration of the relation of
physico-chemical structures to biological ones, while they
express the limits of Hamiltonian description in physics.

Indeed, all these problems have a common element: time. Maybe the
orientation of my work came from the conflict which arose from my
humanist vocation as an adolescent and from the scientific
orientation I chose for my university training. Almost by
instinct, I turned myself later towards problems of increasing
complexity, perhaps in the belief that I could find there a
junction in physical science on one hand, and in biology and
human science on the other.

In addition, the research conducted with my friend R. Herman on
the theory of car traffic^{50} gave me
confirmation of the supposition that even human behaviour, with
all its complexity, would eventually be susceptible of a
mathematical formulation. In this way the dichotomy of the "two
cultures" could and should be removed. There would correspond to
the breakthrough of biologists and anthropologists towards the
molecular description or the "elementary structures", if we are
to use the formulation by Lévi-Strauss, a complementary move
by the physico-chemist towards complexity. Time and complexity
are concepts that present intrinsic mutual relations.

During his inaugural lecture, De Donder spoke in these
terms:^{51} "Mathematical physics
represents the purest image that the view of nature may generate
in the human mind; this image presents all the character of the
product of art; it begets some unity, it is true and has the
quality of sublimity; this image is to physical nature what music
is to the thousand noises of which the air is full..."

Filtrate music out of noise; the unity of the spiritual history
of humanity, as was stressed by M. Eliade, is a recent discovery
that has still to be assimilated.^{52}
The search for what is meaningful and true by opposition to noise
is a tentative step that appears to be intrinsically related to
the coming into consciousness of man facing a nature of which he
is a part and which it leaves.

I have many times advocated the necessary dialogue in scientific
activity, and thus the vital importance of my colleagues and
collaborators in the journey that I have tried to describe. I
would also stress the continuing support that I received from
institutions which have made this work a feasible one, especially
the Université Libre de Bruxelles and the University of
Texas at Austin. For all of the development of these ideas, the
International Institute of Physics and Chemistry founded by E.
Solvay (Brussels, Belgium) and the Welch Foundation (Houston,
Texas) have provided me with continued support.

The work of a theoretician is related in a direct way to his
whole life. It takes, I believe, some amount of internal peace to
find a path among all successive bifurcations. This peace I owe
to my wife, Marina. I know the frailty of the present, but today,
considering the future, I feel myself to be a happy man.

From *Nobel Lectures, Chemistry 1971-1980*, Editor-in-Charge Tore Frängsmyr, Editor Sture Forsén, World Scientific Publishing Co., Singapore, 1993

This autobiography/biography was written
at the time of the award and first
published in the book series *Les
Prix Nobel*.
It was later edited and republished in *Nobel Lectures*. To cite this document, always state the source as shown above.

*Ilya Prigogine died on May 28, 2003.*

Copyright © The Nobel Foundation 1977

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