Customer Reviews (1)

A CHALLENGING "POPULAR" WORK BY A NOBEL LAUREATE
Ilya Prigogine (1917-2003) was a Russian-born naturalized Belgian physical chemist and Nobel Laureate noted for his work on dissipative structures, complex systems, and irreversibility.This 1980 book was perhaps his first work intended for a "general reader" (see his Order Out of Chaos, Is Future Given?, and The End of Certainty for later, easier-to-read books).

He has three main theses: (1) "irreversible processes are as REAL as reversible ones." (2) "irreversible processes play a fundamental CONSTRUCTIVE role in the physical world." (3) "irreversibility is deeply rooted in dynamics." He adds, "This formulation leads to a unified picture that enables us to relate many aspects of our observations of physical systems to biological ones. The intention is not to 'reduce' physics and biology to a single scheme, but to clearly define the various levels of description and to present conditions that permit us to pass from one level to another."

One of his key paragraphs (pg. 83-84) is this: "Biological order is both architectural and functional; furthermore, at the cellular and supercellular levels, it manifests itself by a series of structures and coupled functions of growing complexity and hierarchical character. This is contrary to the concept of evolution as described in the thermodynamics of isolated systems, which leads simply ... to 'disorder.' ... The unexpected new feature is that nonequilibrium may ... lead to a new type of structure, the DISSIPATIVE structures, which are essential in the understanding of coherence and organization in the nonequilibrium world in which we live."

He suggests, "most biological mechanisms of action show that life involves far-from-equilibrium conditions beyond the stability of the threshold of the thermodynamic branch. It is therefore very tempting to suggest that the origin of life may be related to successive bifurcations that have led to a state of matter of increasing coherence."He later states, "Therefore, we can now recognize ourselves as a kind of evolved form of dissipative structure..." (pg. 123)

Turning to the subject of cosmology, he writes, "However, the questions, What is irreversibility on the cosmic scale? Can we introduce an entropy operator in the framework of a dynamical description in which gravitation plays an essential role? are formidable ones. I prefer to confess my ignorance." (pg. 214)

He concludes, "At the origin of thermodynamics we find 'negative' statements expressing the impossibility of certain transformations. In many textbooks, the second law of thermodynamics is expressed as the postulate that it is impossible to transform heat into work using a single thermostat. This negative statement belongs to the macroscopic world--in a sense we have followed its meaning to the microscopic level when it becomes, as we have seen, a statement about the observability of the basic conceptual entities of classical or quantum mechanics. As in relativity, a negative statement is not the end of the story: it leads in turn to new theoretical structures." (pg. 215)

This is a complex and challenging work by a major thinker of the 20th century. ... Read more

Product Description
Unexpected discoveries in nonequilibrium physics and nonlinear dynamics are changing our understanding of complex phenomena. Recent research has revealed fundamental new properties of matter in far-from-equilibrium conditions, and the prevalence of instability-where small changes in initial conditions may lead to amplified effects. ... Read more

Customer Reviews (4)

if you want detailed proofs, go elsewhere
decent overview, but not to be read as a math text.
lots of holes and gaps in the mathematical treatment.
if you are interested in pattern formation, try "the self made tapestry" by ball.nice book. (not mathematical.)

A Foundation of Complexity
I do strongly agree with the first reviewer that the most effective way to get into complexity is to start with the original! At present, the complexity theory is overwhelming - covering the application ranging from physics to social sciences.

However, I think only few people outside the mainstream of sciences know that the origin of this theory is from the "Brussel School of Thought" pioneering by Theophile De Donder and perfecting by Ilya Prigogine and his colleagues in the past century. All of whom were working on non-equilibrium and statistical thermodynamics.

Perhaps, the greatest contribution this group of scientists (the majority of which are physical chemists) have made is the discovery of order that can sponteneously arise out of randomness through the influx of energy and the export of entropy. This idea has been further elaborated and developed into the theory of dissipative structures in which the dynamics of complex systems are described and explained.

For the general readers, I would recommend "Order out of Chaos: Man's New Dialogue with Nature" (Prigogine and Stengers, 1984) as a primer before going into this volume. The early chapters of "The Self-Organizing Universe: Scientific and Human Implications of the Emerging Paradigm of Evolution" (Jantsch, 1979) also helps.

This book is a concise and comprehensive introduction to the the field of complexity. A prior knowledge on non-equilibrium and statistical thermodynamics and non-linear dynamics will be a great help, but not compulsory, to appreciate this work and I would recommend this book to the readers with technical backgrounds and want to get into the field of complexity in a serious fashion.

Doy Sundarasaradula
May 9, 2009

Intuitive view about the emergence of complexity
It explains, mainly through examples in chemistry and physics, what are the required components for "complex behaviors" to occur within dynamical systems. It does not insist on the technicalities proper to the examples but rather tries to gather what one can learn from specific situations concerning the necessary components for complexity to arise.

Focus is on intuition and global understanding, not on mathematical aspects. However, some knowledge in math would certainly help...a first course in probability theory and some background in dynamical systems is a good idea (at the level of undergraduate courses in pure and applied sciences).

All explanations are not rigorous but the objective is to provide a good intuition about the mechanisms driving complexity. Recommended for all people interested in stochastic modeling and chaos theory.

Want to learn about complexity? Start at the source!
Since non-equilibrium science and complexity theory where actually shaped and influenced by the Brussels school, anybody interested in a concise -yet readable- introduction would do well to start with this book. Written byNicolis and Prigogine, it will enlighten and entertain you. Some knowledgeof math helps when reading this book, but the level is intermediate,thereby making it suitable for a rather large group of interested readers.I found myself reading the book in stages, taking the time to pondervarious topics and issues before continuing again. It really made mewonder, and I learned a lot from it (ironically, I actually learned morefrom this book than from the -much- more advanced books by the author(s)that cover the same material). ... Read more

Product Description
Time, the fundamental dimension of our existence, has fascinated artists, philosophers, and scientists of every culture and every century. All of us can remember a moment as a child when time became a personal reality, when we realized what a "year" was, or asked ourselves when "now" happened. Common sense says time moves forward, never backward, from cradle to grave. Nevertheless, Einstein said that time is an illusion. Nature's laws, as he and Newton defined them, describe a timeless, deterministic universe within which we can make predictions with complete certainty. In effect, these great physicists contended that time is reversible and thus meaningless.Amazon.com Review
In this intellectually challenging book, Nobel laureate Ilya Prigogine tackles some of the difficult questions that bedevil physicists trying to provide an explanation for the world we observe. How is it, for instance, that basic principles of quantum mechanics--which lack any differentiation between forward and backward directions in time--can explain a world with an "arrow of time" headed unambiguously forward? And how do we escape classical physics' assertion that the world is deterministic? In a sometimes mathematical and frequently mind-bending book, Prigogine explores deterministic chaos, nonequilibrium thermodynamics, and even cosmology and the origin of the universe in an attempt to reach an explanation that can reconcile physical laws with subjective reality. ... Read more

Customer Reviews (17)

A new formulation of the fundamental laws of physics
In this iconoclastic book, Ilya Prigogine argues for a concept of total indeterminacy by incorporating time in the current deterministic scientific laws.

Time in modern physics
Ilya Prigogine observes that the time dimension incorporated in the basic laws of physics, the classical Newtonian dynamics, relativity or quantum physics, does not make a distinction between the past and the future. There is no arrow of time, as in chemistry, geology, biology or the humanities. However, we should incorporate an evolutionary aspect (indeterminacy) in our physical laws, by revising the concept of time.

Revision of the concept of time in physics
The physics of non-equilibrium processes study dissipative systems, which are characterized by a one-dimensional, irreversible time (e.g. eddies, laser radiation, oscillations). This irreversibility is an essential condition for consistent behaviors in populations of trillions of trillions of molecules.

Revision of the deterministic physical laws
It becomes possible to overcome the contradictions between the reversible laws of dynamics and the evolutionary description associated with entropy, by extending dynamics to unstable and chaotic systems.
At and around the equilibrium, the laws of nature maintain their universality. Far from the equilibrium, they depend on the type of unstable irreversible processes. This instability can be incorporated into the basic laws with the introduction of statistics. Thus, the laws of nature become pure possibilities. There are no certainties any more. The laws describe a `becoming' not a `being'.
Irreversibility may lead to the formation of molecules which could not be synthesized in conditions close to equilibrium. In this case, she becomes a part of matter.

An eternal time?
Irreversible processes associated with dynamic instabilities have played a decisive role in the universe since its birth. In this perspective, time is eternal: it has neither a beginning nor an end. We could create a theory which combines certain elements of the two traditional cosmological models, the steady state and the big bang. The first model would be applicable to the pre-universe, an unstable environment that produced our universe, while the second would apply specifically to our universe.

This controversial book is a must for anyone interested in contemporary physics.

great
As always Prigogine cuts to the core of the problem of analyzing complex dynamical systems

I am happy
This is one of the best books which I have ever read in my life.

His most detailed updated book
by the late Nobel Laureate on the controversial issue of time's arrow. It's not clear he succeeded but his passion was never missing. He has consistently held in his books that nature is probabilistic even though his explanation of the 2nd law of thermodynamics, that entropy can only hold constant or increase in an isolated system, has evolved. (For instance in acceding to Frank Tipler that gravity breaks invariance.) Much of his motivation seems to have been in sorting out why Boltzman and Gibbs failed to satisfy the science community that their statistical physics explained the 2nd law, due to reversible classical equations and Poincare recurrences. However in order to make his probabilistic argument he may have created a loophole. He points to the Langevin equation as an irreversible equation with noise (friction) and he says Poincare should have connected nonintegrability with irreversibility and most dynamics are nonintegrable. However everyone agrees some (simple) systems are reversible (pendulums etc) so how can all of nature be stochastic? Maybe because the noise terms tend to but never go to zero? However in addressing the arrow of time he suggests gravity which is ignored in thermodynamics as are all interactions; but this explanation is also used by others in deterministic models. So it may never be provable who is right; but if his loophole is real I think there may be a simpler explanation.

Statistical entropy in all of it's variations is an excellent inference tool but it is about an observer's measurements and not underlying properties of the system being measured (frequentist approaches come close but usually have to extrapolate). In this case Poincare recurrence maybe non-physical, a mere statistical fluctuation with no actuality. (Prigogine says it is false because he introduces new microscopic dynamics, I'm just saying it may not arise in reality but only through statistical assumptions which depend on observer uncertainty.) I agree with the explanation at the website secondlaw.com that the thermodynamic explanation of entropy is fundamental as it is a measure of energy diffusion, and not randomness or uncertainty as the tool of statistical entropy would imply. In this way the 2 approaches are not contradictory; the statistical is merely a measurement tool for observers while the thermodynamic is real dynamics requiring no observers (ice melts, water crystalizes etc long before man was around). The current argument in wikipedia that statistical entropy is considered more fundamental because the others can be derived from it is silly; there are many types of subjective entropy measures, the basic frequentist vs Bayesian approaches, there is volume entropy such as for measuring expanding gases, configurational entropy such as for crystals etc; however there is only one thermodynamic entropy, Clausius's dS = <>q/T (for reversible systems; calculations change of course with potential variables of volume, pressure and temperature). If anything this should be viewed as fundamental as it is a direct measurement of the physical movement of heat. One should not confuse information theory and measurement techniques with real underlying dynamics. When some authors say 'entropy is not a property of a system, it is a property of our description of the system' they are referring to statistical entropy measures and not real thermodynamics. As Prigogine says 'irreversability is not just in our minds', that it applies to nonintegral systems identified by Poincare but not the connection. The very same wikipedia current description, possibly by a different author, accedes the point: "The problem with linking thermodynamic entropy to information entropy is that in information entropy the entire body of thermodynamics which deals with the physical nature of entropy is missing...information entropy gives only part of the description of thermodynamic entropy. Some, authors, like Tom Schneider, argue for dropping the word entropy for the H function of information theory and using Shannon's other term 'uncertianty' instead."


If Boltzman had accepted that his equation was not fundamental but an inference tool then most of the debates would likely not have arisen, including Prigogine's criticism of an excellent tool that did not deserve to be criticized on that basis. However what he has done is to show mathematically how irreversibility can apply at the microscopic level for nonintegral systems (in agreement with macroscopics) due to non-local persistent interactions but has to be measured statistically at the level of ensembles and not individual trajectories. This is quite a feat even if controversial. Nevertheless the standard entropy calculations apply for equilibrium systems and the arrow of time is still mysterious though possibly linked to gravity as he says. It would have been nice to see some discussion of entropy of non-equilibrium systems for which there is no universal agreement. For instance it is said that 'the rate of change of entropy with time for a nonequilibrium stochastic process is always positive.' [B.C. Bag; the following references are also available on the net with a simple author search.] This might suggest he already solved the problem and gravity is not required? But-

R. Metzler et. al. say 'Prigogine introduced novel microscopic laws which are irreversible with time. One reason for this ongoing discussion is the absence of rigorous mathematical proofs of irreversible properties in the thermodynamic limit...ensemble averages do not give a basic explanation of irreversible properties, since they contain an average over infinitely many trajectories. Ergodic theory does not help either, since it needs time averages over infinitely many trajectories...In this model we introduce a model with deterministic time reversible dynamics which can be analysed in detail...The Poincare return time is known exactly...' However this takes us back to the usual complaints about statistical fluctuations. [Is there a real arrow of time if everything is eventually reversible?]

Castagnino and Lombardi have developed an interesting approach to the question of the arrow of time. [Clearly Prigogine failed by his own admission and his gravity conjecture!] 'In fact time reversal invariant equations can have irreversible solutions. [e.g. the pendulum is time-reversal invariant...however the trajectories...are irreversible...]...The traditional local approach owes its origin to the attempts to reduce thermodynamics to statistical mechanics...[however] only by means of global considerations can all decaying processes be coordinated. This means that the global arrow of time plays the role of the background scenario where we can meaningfully speak of the temporal direction of irreversible processes, and this scenario cannot be built up by means of local theories that only describe phenomena confined in small regions of spacetime...the geometrical approach to the problem of the arrow of time has conceptual priority over the entropic approach, since the geometrical properties of the universe are more basic than its thermodynamic properties.'

Obviously the debate continues. While Prigogine may not have solved the arrow of time, his work on correlations is important as these are assumed away in classical physics but they are critical to life!

OK writing, great science
Reading this "popular science" book, written by one of the greatest contemporary chemical physicists, was both difficult and satisfying. To avoid a fit of sycophancy, let's just say that I wish I had it when taking my postgrad Statistical Mechanics class. The only negative thing I can cay about this book is that the discussion is somewhat eclectic; it often oscillates between almost trivial philosophy and very high-level, cutting-edge science. It is not clear what the reader is expected to know before starting on this book. That said, if you can work your way through it, you will likely come out with a new understanding of non-equilibrium statistical mechanics and the physics of complex systems.
... Read more

Customer Reviews (6)

Bad Philosophical Work
I will immediately reveal my bias against this book: there is a vast literature that has been developed over the last century on the philosophy of Science, with many insightful contributions from scientists and philosophers alike. Why then is Prigogine and company citing Heidegger in the main? I'm not making the claim that one must be a scientist to be a good philosopher of science (Heidegger was not a scientist), but why the large scale neglect? The result is that the authors' BIG claims about science are not well supported and they carry very little force on their own.

Furthermore, the quality of the writing is poor. A general example of what I find wrong with the writing is this: the authors make many sweeping statements like "science tells us such and such" (page you wonder? Nearly every page). But two scientific theories can be contradictory when taken together -- relativity and quantum mechanics is a well known example of this. So what science tells us in this case is trivial. This is because anything is derivable from a contradiction and a contradiction is the result when we lump all scientic theories together under one general heading "Science." More appropriately, then, we would say "scientific theory A tells us X and scientific theory B tells us Y", etc. When carrying out a technical discussion, such as one about science, sciences, and scientific methodology, there is a demand for discursive precision. This precision is completely lacking here.

Another distinction that is useful -- one never mentioned -- is that science is a normative framework for building theories, not a theory itself that tells us anything about the world. Theories are the deductive structures where we make conclusions, true or false, about some phenomenom. If my analysis of science as a normative framework is not agreeable to the author there are still other distinctions that could be made about science that could clean up the discussion radically. Who cares about the discussion of dynamic systems when the thesis is so problematic? Two stars is generous.

Greater than Newton
Prigogine (and the philosopher and chemist Isabelle Stengers) I met in Order out of Chaos (1984, French original La nouvelle alliance 1979) and later in many other books. About "modern" analytical-reductionist science from the 17th century it is said in the book: "Nature's humiliation is parallell to the glorification of whatever escapes it, God and man" (p. 53 in the Swedish translation from 1984). The depreciation of nature unites science and religion. But life is "the outermost consequence of the occurrence of self-organizing processes, instead of being something outside nature's order" (172). We are the last creation of the nature we learnt to despise. "The classical science", it is said summarizing, "the mythical science about a simple, passive world, belongs to the past, killed not by philosophical criticism or empirical resignation but by the internal development of science itself" (57).
With the help of Prigogine's theory, covering both matter and life, we can overcome the biases of natural science and humanities. For natural science deals with a world without Man, the humanities - and still more "humanism" - with Man without world. The first case can be felt to be poor and inane and the second one to be narrow-minded and anthropocentric. This depends on the fact that in both cases it is a question of abstraction and construction. For the world is one only, it is only we who persist in dividing it into two: Man and Nature, soul and body, mind and matter.
So it becomes urgent to contemplate the relationships between both sides, something I did already in my doctoral dissertation, Landscape and Nature in [Selma Lagerlöf's] Gösta Berling's Saga and the Wonderful Adventures of Nils (in Swedish). That is why it is such a bliss to work and (re)search in the way I do now. And whoever understood how to focus wholeness and process in a great novel and so succeeded to grasp its way of functioning also got prerequisitions to understand big and small systems in the world, from the whirl and the candle light to Earth as a geological-biological organisation. The way of thinking is the same. And evolution runs from matter to man.
Ilya Prigogine (1917-2003) was professor in physical chemistry in Brussels and Austin, Texas. He got the Nobel prize in chemistry in 1977. From an early interest in the humanities he went to a career in natural science, a career that made him the Newton of our time. In contrast to the first Newton, he despises a worldview that does not enclude both Nature and Man (including the scientist himself). And since Prigogine created such a world-view that is adequate and valid, he can be said to be greater than Newton.

A thorough study of the history of quantum physics and an exhaustive description of how order emerges from chaos
Prigogine describes his ideas of how order emerged from a ground of chaos and how the processes of entropy can lead a system open to its environment to evolve greater complexity.He also gives an exposition of the relevance of science to society.Prigogine's Nobel prize-winning models of dissipative structures are difficult to understand but persistent effort will reward the reader.His theories are as applicable to the evolution and expansion of consciousness as to the emergence of life on earth from a relatively simple environment.

A classic on self-organization
This work is one of the classics of the breakthrough period of chaos theory, complex systems, and self-organization theories. Mixing two modes and two cultures it stretches its bow between the nitty-gritty details of dissipative systems, and the history of the relations of the human and natural sciences, from the age of the emergence of thermodynamics to the present. The book has something now routinely filtered from discussion, the early critiques of the Newtonian mindset as it was starting to become dominant. The material on the history of the two cultures would seem to fall on deaf ears these days, and gives the book at depth not often seen in works of this type. Very much worth reading.

Dissipative structures what? Chaos
The whole problem with writing about a book, and especially this one, is that one has to cut a long story short. A story long enough to encompass a fair amount of scientific history - elaborated, if not referenced exhaustively. Not that it is meant to be. Prigogine's journey does not offer to take you by the hand for a guided tour of order, complexity and self-organisation. Rather, it keeps to the spirit of Toffler's introduction, (Was it coincidental that it was the other way round?!) where he talks about the wonderful art of scientific dissection. Order out of chaos, however, is a difficult read for the anyone who has been initiated into the scientific non-fiction. For those who expect the book to be a popular account of concepts in complexity and self-organisation, the intense style and the depth of detail can be exhausting. Like Penrose in the Emperor's New Mind, Prigogine's style is uncompromising.Toffler's introduction is fitting, if only in parts. The book does not offer explanations. Rather, Prigogine prefers to illumate his readers with his keen philosophical bent. It is here that the book triumphs. The effort that has gone into integrating the ideas in the book, the subtle nuances reflecting Prigogine's own views is truly commendable. But then, one should be fairly conversant with the loopholes that science finds itself in. The description of the behaviour of complex systems warrants some mention. The idea of switching between reality and mathematical description does not gel with the rest of the narrative in parts - specially when chemistry is the running example.Well, Prigogine wasn't writing the book with the intention of it being self-contained - and he makes no bones about it. That is the seed of inspiration, I suppose, for any writer, be it for the cause of science or for the sheer love for the written word.Prigogine has shown that philosophy is in some way inseparable from what many consider the scientist's playground. And we are glad that he has shared his views with us. ... Read more

Product Description
Membranes, Dissipative Structures, and Evolution Edited by G. Nicolis & R. Lefever Focuses on the problem of the emergence/maintenance of biological order at successively higher levels of complexity. Covers the spatiotemporal organization of simple biochemical networks; the formation of pluricellular or macromolecular assemblies; the evolution of these structures; and the functions of specific biological structures. Volume 29 in Advances in Chemical Physics Series, I. Prigogine & Stuart A. Rice, Editors. 1975 Theory and Applications of Molecular Paramagnetism Edited by E. A. Boudreaux & L. N. Mulay Comprehensively treats the basic theory of paramagnetic phenomena from both the classical and mechanical vantages. It examines the magnetic behavior of Lanthanide and Actinide elements as well as traditional transition metals. For each class of compounds, appropriate details of descriptive and mathematical theory are given before their applications. 1976 Theory and Aapplications of Molecular Diamagnetism Edited by L. N. Mulay & E. A. Boudreaux An invaluable reference for solving chemical problems in magnetics, magnetochemistry, and related areas where magnetic data are important, such as solid-state physics and optical spectroscopy. 1976 ... Read more

Product Description
In this book, after discussing the fundamental problems of current science and other philosophic concepts, beginning with controversies between Heraclitus and Parmenides, Ilya Prigogine launches into a message of great hope: the future has not been determined. Contrary to globalisation and the apparent contemporary mass culture society, individual behaviour is beginning to increasingly become the key factor which governs the evolution of both the world and society as a whole. It is a message that challenges existing widespread views, implicitly or explicitly, through mass communication; moreover the importance of the individual's actions implies a reflection of each person on the responsibilities that each one assumes when taking or acting upon a decision. This responsibility is associated with the freedom of thought as well as a critical analysis of fashions, customs, preconceived ideas, and ideologies, externally imposed: exactly contrary to the ideas of those who wish us to be "perfect consumers" in a world dominated only by monetary wealth.

Challenging this drive towards the elimination of freedom of thought in the individual is now imperative if we are to save man and his planet from catastrophe, which seems to be ever imminent and (unfortunately) irreversible.

This last book of Ilya Prigogine provides a small, disputable, but nonetheless valuable contribution towards that end. ... Read more

Customer Reviews (1)

A nice little summary
of the late Nobel prize-winner's book. He has consistently held in his books that nature is probabilistic even though his explanation of the 2nd law of thermodynamics, that entropy can only hold constant or increase in an isolated system, has evolved. Much of his motivation seems to have been in sorting out why Boltzman and Gibbs failed to satisfy the science community that their statistical physics explained the 2nd law, due to reversible classical equations and Poincare recurrences. However in order to make his probabilistic argument he may have created a loophole. He points to the Langevin equation as an irreversible equation with noise (friction) and he says Poincare should have connected nonintegrability with irreversibility and most dynamics are nonintegrable. However everyone agrees some (simple) systems are reversible (pendulums etc) so how can all of nature be stochastic? Maybe because the noise terms tend to but never go to zero? However in addressing the arrow of time he suggests gravity which is ignored in thermodynamics as are all interactions; but this explanation is also used by others in deterministic models. So it may never be provable who is right; but if his loophole is real I think there may be a simpler explanation.

Statistical entropy in all of it's variations is an excellent inference tool but it is about an observer's measurements and not underlying properties of the system being measured (frequentist approaches come close but usually have to extrapolate). In this case Poincare recurrence maybe non-physical, a mere statistical fluctuation with no actuality. (Prigogine says it is false because he introduces new microscopic dynamics, I'm just saying it may not arise in reality but only through statistical assumptions which depend on observer uncertainty.) I agree with the explanation at the website secondlaw.com that the thermodynamic explanation of entropy is fundamental as it is a measure of energy diffusion, and not randomness or uncertainty as the tool of statistical entropy would imply. In this way the 2 approaches are not contradictory; the statistical is merely a measurement tool for observers while the thermodynamic is real dynamics requiring no observers (ice melts, water crystalizes etc long before man was around). The current argument in wikipedia that statistical entropy is considered more fundamental because the others can be derived from it is silly; there are many types of subjective entropy measures, the basic frequentist vs Bayesian approaches, there is volume entropy such as for measuring expanding gases, configurational entropy such as for crystals etc; however there is only one thermodynamic entropy, Clausius's dS = <>q/T (for reversible systems; calculations change of course with potential variables of volume, pressure and temperature). If anything this should be viewed as fundamental as it is a direct measurement of the physical movement of heat. One should not confuse information theory and measurement techniques with real underlying dynamics. When some authors say 'entropy is not a property of a system, it is a property of our description of the system' they are referring to statistical entropy measures and not real thermodynamics. As Prigogine says 'irreversability is not just in our minds', that it applies to nonintegral systems identified by Poincare but not the connection.

If Boltzman had accepted that his equation was not fundamental but an inference tool then most of the debates would likely not have arisen, including Prigogine's criticism of an excellent tool that did not deserve to be criticized on that basis. However what he has done is to show mathematically how irreversibility can apply at the microscopic level for nonintegral systems (in agreement with macroscopics) due to non-local persistent interactions but has to be measured statistically at the level of ensembles and not individual trajectories. This is quite a feat even if controversial. Nevertheless the standard entropy calculations apply for equilibrium systems and the arrow of time is still mysterious though possibly linked to gravity as he says. More details of his derivations are provided in his book The End of Certainty but it would have been nice to see some discussion of entropy of non-equilibrium systems for which there is no universal agreement. For instance it is said that 'the rate of change of entropy with time for a nonequilibrium stochastic process is always positive.' [B.C. Bag; the following references are also available on the net with a simple author search.] This might suggest he already solved the problem and gravity is not required? But-

R. Metzler et. al. say 'Prigogine introduced novel microscopic laws which are irreversible with time. One reason for this ongoing discussion is the absence of rigorous mathematical proofs of irreversible properties in the thermodynamic limit...ensemble averages do not give a basic explanation of irreversible properties, since they contain an average over infinitely many trajectories. Ergodic theory does not help either, since it needs time averages over infinitely many trajectories...In this model we introduce a model with deterministic time reversible dynamics which can be analysed in detail...The Poincare return time is known exactly...' However this takes us back to the usual complaints about statistical fluctuations. [Is there a real arrow of time if everything is eventually reversible?]

Castagnino and Lombardi have developed an interesting approach to the question of the arrow of time. [Clearly Prigogine failed by his own admission and his gravity conjecture!] 'In fact time reversal invariant equations can have irreversible solutions. [e.g. the pendulum is time-reversal invariant...however the trajectories...are irreversible...]...The traditional local approach owes its origin to the attempts to reduce thermodynamics to statistical mechanics...[however] only by means of global considerations can all decaying processes be coordinated. This means that the global arrow of time plays the role of the background scenario where we can meaningfully speak of the temporal direction of irreversible processes, and this scenario cannot be built up by means of local theories that only describe phenomena confined in small regions of spacetime...the geometrical approach to the problem of the arrow of time has conceptual priority over the entropic approach, since the geometrical properties of the universe are more basic than its thermodynamic properties.'

Obviously the debate continues. While Prigogine may not have solved the arrow of time, his work on correlations is important as these are assumed away in classical physics but they are critical to life!
... Read more

Product Description
Part of a series devoted to helping the reader obtain general information about a wide variety of topics in chemical physics. Its aim is to present comprehensive analyses of subjects of interest and to encourage the expression of individual points of view. ... Read more

Product Description
Part of a series devoted to helping the reader obtain general information about a wide variety of topics in chemical physics. Its aim is to present comprehensive analyses of subjects of interest and to encourage the expression of individual points of view. ... Read more

Product Description
This series, Advances in Chemical Physics, is devoted to helping the reader obtain general information about a wide variety of topics in chemical physics, which field the editors interpret very broadly. Their intent is to have experts present comprehensive analyses of subjects of interest and to encourage the expression of individual points of view. The editors hope that this approach to the presentation of an overview of a subject will both stimulate new research and serve as a personalized learning text for beginners in the field. ... Read more