I did buy this book some time ago and then I was fascinated. I studied the basis of his theory, but unfortunately, Prigogine passed away recently, before I can discuss with he some topics in more detail.The greater part of the book is written in a natural style, but some sections are highly mathematical even for the majority of scientists! This mathematical presentation has a curious explaining. There are several version of Prigogine's theory, but the first versions had been "abandoned", and then Prigogine details the new approach: "Star-unitary theory for LPS outside of Hilbert space".
An earlier reviewer said that the book provides a solution to three of the most important problems in science: (1) Time's arrow. (2) The measurement problem in QM. (3) The existence of freewill. Precisely, I am working in those and other questions, and I do not believe that claim was completely correct (and perhaps Prigogine believed the same, because in his last communication, said me "The questions that you ask are very difficult."). In my opinion, the novel theory is conflictive both in mathematical and physical details, but I consider that, at least, the aim of the School is correct one. Irreversibility and uncertainty are two fundamental features of our universe. I see that orthodox physics (including particle physics and the so-called String-M theory) is incorrect and/or inapplicable. I believe that, whereas other "popular" books (The Quark and The Jaguar, The Elegant Universe, etc.) should be "relics" in 21st century physics, Prigogine's book will be then a basic work.
The contributions of Prigogine's physics to the understanding in other disciplines, as chemistry, are not clear. In fact, I believe that the impact of recent Prigogine's ideas into fundamental chemistry has been "insignificant", because his revolutionaries ideas in physics are an outcome of their previous chemical investigations (Nobel Prize for Chemistry). For example, in his complex spectral theory, energy is an imaginary quantity, and this is in direct conflict with standard quantum theory postulates. However, in theoretical chemistry, one always defines a transition state by means of an imaginary frequency. As said Prigogine in a recent Solvay conference, "all of Chemistry deals with irreversible processes". I cannot say the same of physics.
The book is very good one, but I disagree in one point. When one writes a scientific paper for publication in a specialized journal (as Physical Review), one can write about everything. Referees and other scientist can either accept or reject your work in scientific grounds. When one writes a popular book for non-expertises, one must be the most "neutral" possible. If this is not possible, one must to "alert" to the reader. This book is not neutral and, in some restricted sense, shows several theories and ideas as been of broad acceptance or current use in science. Of course, this overemphasizes the scientific status of the so-called Brussels School and minimizes the importance of other interesting points of view. In my opinion, this is not a correct attitude. For example, the "diagrammatic" method developed by Brussels School in the 60's (and illustrated in the book) is broadly not used by scientific community. See, for example, "Nonequilibrium Statistical Mechanics" by Robert Zwanzig for a view in more standard formalisms. In addition, I also must say that some previous Prigogine's ideas in dissipative structures, kinetic potentials, etc. are not standard, and other, as the "universal" criterion of evolution (following production of entropy), was experimentally shown to be false. Of course, other contributions of called Brussels School are simply impressive, for example the extension of scattering theory of particle physics to more general situations of chemical kinetics. Effectively, you have read fine, orthodox S-matrix of "fundamental" physics can be derived as an idealized asymptotic version valid for typical accelerator experiments! I am sorry, but I must said that Chemistry is not applied QED.
Conclusion: The book describes an excellent philosophical view in a "new" physics, and for this reason it may be a central piece on your collection. Nevertheless, I consider that the scientific way proposed is a little conflictive and some mathematics may be modified!
