The authors of Order Out of Chaos show that in the machine age, traditional science focuses on stability, order, uniformity and balance. It studies mainly closed systems and linear relationships in which a small input signal causes a small output response. The Prigogine paradigm is especially interesting in that it focuses on aspects of reality that are most characteristic of the modern stage of accelerated social change: disorder, instability, diversity, disequilibrium, non-linear relationships in which a small signal at the input can cause an arbitrarily strong response at the output.
Prigogine's works form a new, comprehensive theory. In a greatly simplified form, the essence of this theory boils down to the following. Some parts of the universe may indeed act as machines. These are closed systems, but at best they constitute only a small fraction of the physical Universe. Most of the systems that are of interest to us are open - they exchange energy or matter (one might add: information) with the environment. Open systems undoubtedly include biological and social systems, which means that any attempt to understand them within the framework of a mechanistic model is certainly doomed to failure.
In my opinion, Prigogine’s book may be of interest to managers as another building block in the formation of a systemic view of organizations (see also James Gleick. Chaos. Creation of a new science).
Prigozhim I., Stengers I. Order from chaos: A new dialogue between man and nature. - M.: Progress, 1986. - 432 p.
To use Prigogine's terminology, we can say that all systems contain subsystems that constantly fluctuate. Sometimes a single fluctuation or combination of fluctuations can become (as a result of positive feedback) so strong that the previously existing organization cannot withstand and collapses. At this turning point (at the bifurcation point), it is fundamentally impossible to predict in which direction further development will occur: whether the state of the system will become chaotic or whether it will move to a new, more differentiated and higher level of order.
The facts discovered and understood as a result of the study of highly nonequilibrium states and nonlinear processes, in combination with rather complex systems endowed with feedbacks, led to the creation of a completely new approach that allows us to establish a connection between the basic sciences and the “peripheral” life sciences and, perhaps, even understand some social processes. (The facts in question are of equal, if not greater, significance to social, economic, or political realities. Words such as “revolution,” “economic crisis,” “technological shift,” and “paradigm shift” take on new shades when we begin to think about the corresponding concepts in terms of fluctuations, positive feedbacks, dissipative structures, bifurcations and other elements of the conceptual vocabulary of the Prigogine school.)
By emphasizing that irreversible time is not an aberration, but a characteristic feature of much of the Universe, Prigogine and Stengers undermine the very foundations of classical dynamics. For the authors, the choice between reversibility and irreversibility is not a choice of one of two equal alternatives. Reversibility (at least if we are talking about sufficiently large periods of time) is inherent in closed systems, irreversibility is inherent in the rest of the Universe.
In the scientific heritage we have inherited, there are two fundamental questions to which our predecessors were unable to find an answer. One of them is the question of the relationship between chaos and order. Banner's 1st law of increasing entropy describes the world as constantly evolving from order to chaos. At the same time, as biological or social evolution shows, the complex arises from the simple. How can structure emerge from chaos? Disequilibrium - the flow of matter or energy - can be a source of order. But there is another, even more fundamental question. Classical or quantum physics describes the world as reversible, static. There is a clear contradiction between the static picture of dynamics and the evolutionary paradigm of thermodynamics. What is irreversibility? What is entropy?
INTRODUCTION CHALLENGE TO SCIENCE
What prerequisites of classical science have modern science managed to get rid of? As a rule, from those that were centered around the fundamental thesis according to which, at a certain level, the world is simple and obeys fundamental laws reversible in time. Such a point of view seems to us today to be an oversimplification. Since the world around us was not built by anyone, we are faced with the need to give a description of its smallest “bricks” (i.e., the microscopic structure of the world) that would explain the process of self-assembly.
We discovered that in nature, it is not the illusory, but the very real irreversibility that underlies most self-organization processes that plays a significant role. Reversibility and hard determinism in the world around us are applicable only in simple limiting cases. Irreversibility and randomness are now considered not as an exception, but as a general rule.
By its nature, our Universe is pluralistic and complex. Structures can disappear, but they can also appear. Some processes, with the existing level of knowledge, can be described using deterministic equations, while others require the use of probabilistic considerations. According to the previously existing tradition, fundamental processes were considered to be deterministic and reversible, and processes that were in one way or another associated with randomness or irreversibility were interpreted as exceptions to the general rule. Nowadays we see everywhere how important the role played by irreversible processes and fluctuations is. The models considered by classical physics correspond, as we now understand, only to limiting situations. They can be created artificially by placing the system in a box and waiting until it reaches a state of equilibrium. Artificial can be deterministic and reversible. The natural certainly contains elements of chance and irreversibility. This remark leads us to a new perspective on the role of matter in the Universe. Matter is no longer a passive substance described within the framework of a mechanistic picture of the world; it is also characterized by spontaneous activity.
None of the contributions to the treasury of science made by thermodynamics can compare in novelty with the famous second law of thermodynamics, with the advent of which the “arrow of time” first entered physics. The concept of entropy was introduced to distinguish reversible processes from irreversible ones: entropy increases only as a result of irreversible processes. A remarkable feature of the processes we are considering is that in the transition from equilibrium conditions to highly nonequilibrium ones, we move from the repeating and general to the unique and specific.
In the first two parts of our book, we consider two opposing views of the physical world: the static approach of classical dynamics and the evolutionary view based on the use of the concept of entropy. The confrontation between the timeless approach of classical mechanics and the evolutionary approach became inevitable. The third part of our book is devoted to the acute clash of these two opposing approaches to describing the world.
Is there something specific in the structure of dynamic systems that allows them to “distinguish” the past from the future? What is the minimum complexity required for this? Boltzmann already understood that there must be a close connection between probability and irreversibility. The distinction between past and future, and therefore irreversibility, can only enter into the description of a system if the system behaves in a sufficiently random manner. The arrow of time is a manifestation of the fact that the future is not given.
Once I passed by the book “Order from Chaos” by Ilya Prigozhin. I read it yesterday - I was simply delighted! From the standpoint of physics, Prigogine writes about the same epigenetics, about the same adaptability as Waddington and Schmalhausen! It's nice to have such a person behind you :)
Below are some interesting quotes (numbered according to the 1986 edition of Progress):
p.194
At the origins of nonlinear thermodynamics lies something quite surprising, a fact that at first glance is easy to mistake for failure: despite all attempts, generalizing the theorem of minimum entropy production to systems in which the flows are no longer linear functions of forces has proven impossible. Far from equilibrium, the system can still evolve to some stationary state, but this state is, generally speaking, no longer determined by a properly chosen potential (analogous to entropy production for weakly nonequilibrium states). The absence of a potential function poses the question: what can be said about the stability of the states to which the system evolves? Indeed, as long as the attractor state is determined by the minimum potential (for example, entropy production), its stability is guaranteed. True, fluctuations can bring systems out of this minimum. But then the second law of thermodynamics will force the system to return to its original minimum. Thus, the existence of a thermodynamic potential makes the system “immune” to fluctuations. Having the potential, we describe a “stable world” in which systems, as they evolve, move into a static state established for them once and for all.
p.195
Sometimes, Lucretius wrote, at the most uncertain times and in the most unexpected places, the eternal and universal fall of atoms experiences a slight deviation - “clinamen”. The emerging vortex gives rise to the world, to all things in nature. The "clinamen", a spontaneous, unpredictable deflection, has often been criticized as one of the most vulnerable points in Lucretian physics, as something introduced ad hoc. In fact, the opposite is true: “clinamen” is an attempt to explain phenomena such as the loss of stability of laminar flow and its spontaneous transition to turbulent flow. Modern hydrodynamicists test the stability of fluid flow by introducing a perturbation that expresses the influence of molecular chaos, which is superimposed on the average flow. We are not that far from Lucretius’s “clinamen”!
p.198
Thus, the interaction of the system with the outside world, its immersion in nonequilibrium conditions can become the starting point in the formation of new dynamic states - dissipative structures. The dissipative structure corresponds to some form of supermolecular organization. Although the parameters describing crystal structures can be derived from the properties of the molecules that form them, and in particular from the range of action of the forces of mutual attraction and repulsion, Bénard cells, like all dissipative structures, essentially reflect the global situation in the nonequilibrium system generating them. The parameters that describe them are macroscopic - on the order of not 10-8 cm (like the distances between molecules in a crystal), but several centimeters. The time scales are also different: they correspond not to molecular scales (for example, periods of vibration of individual molecules, i.e. about 10-15 s), but to macroscopic ones, i.e. seconds, minutes or hours.
p.209
On the other hand, in many examples of self-organization known from biology, the reaction scheme is simple, while the molecules involved in the reaction of substances (proteins, nucleic acids, etc.) are very complex and specific. The difference we noted is unlikely to be accidental. It reveals a certain primary element inherent in the difference between physics and biology. Biological systems have past. The molecules that form them are the result of previous evolution; they have been selected to participate in autocatalytic mechanisms designed to give rise to very specific forms of organizing processes.
p.216-218
At a certain value of B we reach the stability threshold of the thermodynamic branch. This critical value is usually called the bifurcation point. Let's look at some typical bifurcation diagrams. At bifurcation point B, the thermodynamic branch becomes unstable with respect to fluctuation. At a critical value Lc of the control parameter L, the system can be in three different stationary states: C, E and D. Two of them are stable, the third is unstable. It is very important to emphasize that the behavior of such systems depends on their background. By starting with small values of the control parameter L and slowly increasing them, we are likely to describe the ABC trajectory. On the contrary, starting with large values of concentration X and maintaining a constant value of the control parameter L, we will with a high probability arrive at point D. Thus, the final state depends on the prehistory of the system. Until now, history has been used in the interpretation of biological and social phenomena. Quite unexpectedly, it turned out that prehistory can also play a role in simple chemical processes.
p.219
One would expect that if the experiment is repeated many times when passing through the bifurcation point, on average, in half the cases the system will end up in a state with a maximum concentration on the right, and in half of the cases in a state with a maximum concentration on the left. Another interesting question arises. In the world around us, some simple fundamental symmetries are broken
p.222
It is important to note that depending on the chemical process responsible for the bifurcation, the mechanism described above may be unusually sensitive. As already mentioned, the substance acquires the ability to perceive differences that are imperceptible under equilibrium conditions. Such high sensitivity suggests the idea of simple organisms, such as bacteria, which are known to respond to electric or magnetic fields. More generally, this means that in highly nonequilibrium chemistry, “adaptation” of chemical processes to external conditions is possible. In this way, a strongly nonequilibrium region is strikingly different from an equilibrium region, where the transition from one structure to another requires strong perturbations or changes in boundary conditions.
p.223-224
In such situations, a random fluctuation in the external flow, often called noise, is by no means an annoying hindrance: it gives rise to qualitatively new types of regimes, the implementation of which would require incomparably more complex reaction schemes under deterministic flows. It is also important to remember that random noise is inevitably present in the flows in any “natural system”.
p.230
We could consider that the main mechanism of evolution is based on the play of bifurcations as mechanisms for probing and selecting chemical interactions that stabilize one or another trajectory. This idea was put forward about forty years ago by the biologist Waddington. To describe stabilized paths of development, he introduced a special concept - creod. According to Waddington, the creed had to correspond to possible paths of development arising under the influence of the double imperative - flexibility and reliability.
p.240
Long-range correlations organize the system even before macroscopic bifurcation occurs. We return again to one of the main ideas of our book: disequilibrium as a source of order. In this case the situation is especially clear. In an equilibrium state, molecules behave independently: each of them ignores the others. Such independent particles could be called hypnons (“somnambulists”). Each of them can be as complex as desired, but at the same time “not notice” the presence of other molecules. The transition to a nonequilibrium state awakens hypnons and establishes coherence that is completely alien to their behavior under equilibrium conditions.
Book Order out of chaos published in Russian in 1986. It turned out that at that time I did not read it and I was able to catch up only now. I must say that I liked Prigogine’s ideas: dissipative systems in a highly nonequilibrium state, self-organization and all that. I even saw Prigozhin - he gave a report at Moscow State University. True, Prigozhin decided that he spoke Russian well and began to give a report in Russian. At the same time, no one dared to translate from Russian into Russian.
The book touches on many topics. Much attention is paid to dissipative systems, fluctuations, attractors and bifurcations. I will focus on only one topic: the contrast between mechanics and thermodynamics. This topic is currently somehow eluding attention. Today you can often hear that quantum mechanics and the general theory of relativity are incompatible with each other, but practically nothing is heard about the contradiction between mechanics and thermodynamics.
The contradiction is as follows. The macrosystem consists of atoms that obey the equations of mechanics, and the equations of mechanics are reversible with respect to time. At the macrosystem level, there is entropy, which defines the arrow of time, that is, the second law of thermodynamics prohibits time reversal at the macrosystem level. The question arises of how, based on time-reversible mechanical equations, one can explain the appearance of entropy, which defines the arrow of time. There are three possible solutions:
- The equations of mechanics are absolutely correct, and the appearance of the arrow of time and entropy is associated with the peculiarities of human perception of nature. Energy is objective, and entropy is subjective.
- Entropy is objective, therefore thermodynamics leads to the need to correct the equations of mechanics.
- Convince yourself that although at the level of the microworld everything is reversible in time, an increase in degrees of freedom necessarily leads to the emergence of a fundamental new property - entropy - and, accordingly, the arrow of time.
The book by Prigogine and Stengers examines the relationship between mechanics and thermodynamics through the history of the two disciplines. I liked this approach, it does a good job of showing how people's opinions changed over time.
From the history of the emergence of Newton’s laws, I liked the following episode:
‘Needham talks about the irony with which the enlightened Chinese of the 18th century. met Jesuit reports about the triumphs of European science of that time. The idea that nature obeys simple, knowable laws was hailed in China as an unparalleled example of anthropocentric stupidity.’
This is why the Chinese missed the scientific and technological revolution. Voltaire's quote perfectly expresses the idea of a true Newtonian:
‘...everything is governed by immutable laws...everything is predetermined...everything is necessarily conditioned...There are people who, frightened by this truth, admit only half of it, like debtors handing over half of their debt to creditors with a request to postpone the payment of the rest. Some events, such people say, are necessary, others are not. It would be strange if part of what happens should happen, and another part should not happen... I must certainly feel an irresistible need to write these lines, you - an equally irresistible need to condemn me for them. We are both equally stupid, both are nothing more than toys in the hands of predestination. Your nature is to do evil, mine is to love the truth and publish it in spite of you.’
Prigogine and Stengers do not like this position - they adhere to the second solution, that thermodynamics necessarily says that the laws of mechanics must be adjusted. The book delights in describing the discovery of Fourier's law of heat transfer. This was the first strong blow to the Newtonians, since the Fourier equation, unlike the equations of mechanics, is irreversible in time. Supporters of mechanics tried to change Fourier's law, but nothing worked; heat remained to live according to its own laws. This was followed by the discovery of the second law of thermodynamics and a discussion began on how to resolve the contradiction that arose.
The book examines in detail the work of Ludwig Bohlmann, who wanted to show that the laws of mechanics at the microworld level are compatible with the appearance of entropy at the macrosystem level (third solution). However, the criticism of Poincare, Zermelo and Loschmidt showed that Boltzmann's constructions are inconsistent. Boltzmann acknowledged the criticism and changed his point of view - he became a supporter of the first solution, when the arrow of time and entropy are associated with the peculiarities of human perception of the world.
It should be said that little has changed since the book was published. Currently, all three positions can be found. The first position about the subjectivity of entropy is especially common among physicists who identify entropy in the Boltzmann equation with information in the Shannon equation.
Carlo Rovelli in the book Time order chose Boltzmann's path. Time does not belong to fundamental reality and the universe, but is associated with the peculiarities of perception. Sean Carroll in the book The Big Picture: Towards the Origins of Life, Meaning, and the Cosmos Itself sets out the third solution. At first there was a low-entropy state, then more probable states corresponding to an increase in entropy are obtained. Lee Smolin in the book Return of time essentially close to the second solution.
I would say that the book places too much emphasis on classical statistical mechanics and too little on quantum mechanics. In statistical mechanics, based on classical mechanics, many paradoxes and discrepancies with experimental results arose from the very beginning. We can say that this implicitly indicated that classical mechanics is inapplicable to the description of the microworld. On the other hand, when moving to quantum mechanics, the general question arises of how a classical macrosystem is obtained from a wave function at the microworld level. Maybe the problem of interpreting quantum mechanics and the contradiction between thermodynamics and mechanics are somehow related.
I note that there are many interesting quotes in the book. Below are a few quotes I particularly liked.
Description of the scientist given by Albert Einstein in his congratulatory speech on the 60th birthday of Max Planck ( Motives for scientific research):
‘Most of them are strange, withdrawn, solitary people; Despite these similarities, they are actually more different from each other than the exiles. What brought them to the temple?... one of the most powerful impulses leading to art and science is the desire to escape everyday life with its painful rigidity and inconsolable emptiness, to escape the bonds of the ever-changing whims of one's own. This reason pushes people with subtle spiritual strings from personal experiences into the world of objective vision and understanding. This reason can be compared to the longing that irresistibly draws the city dweller from a noisy and turbid environment to the quiet high-mountain landscapes, where the gaze penetrates far through the still, clean air and enjoys calm outlines that seem destined for eternity.
But to this negative reason there is also a positive one. A person strives in some adequate way to create a simple and clear picture of the world in himself in order to break away from the world of sensations, in order to, to a certain extent, try to replace this world with a picture created in this way.’
Poems by John Doney (1572-1631), in which he lamented the Aristotelian world destroyed by the Copernican revolution:
‘The new philosophers question everything,
The formidable element - fire - has been withdrawn from circulation.
The man has lost his mind - what was not, what was,
It is not the Sun that circles the Earth, but the Earth that revolves around the luminary.
All people honestly admit: our whole world has gone to dust,
When the sages broke it in one fell swoop.
Looking everywhere for something new (doubt is the light in the window),
They destroyed the whole world, down to the pebble, down to the crumb.’
To conclude, a quote from Charles Peirce in relation to the heat death of the universe:
‘You’ve all heard about energy dissipation. It has been discovered that during any transformation of energy, part of it turns into heat, and heat always tends to equalize the temperature. Under the influence of its own necessary laws, the energy of the world is running out, the world is moving towards its death, when forces cease to operate everywhere, and heat and temperature are distributed evenly...
But while no force can resist this tendency, chance can and will hinder it. Force is ultimately dissipative, randomness is ultimately concentrated. The dissipation of energy according to the immutable laws of nature, by virtue of the same laws, is accompanied by circumstances that are more and more favorable for the random concentration of energy. A moment will inevitably come when the two trends balance each other. This is the state in which the whole world undoubtedly finds itself today.’
Information
Ilya Prigogine, Isabella Stengers, Order out of chaos. A new dialogue between man and nature, Moscow, Progress, 1986.
“In our time, both physics and metaphysics actually jointly come to the concept of the world (how! it turns out that metaphysics rules... your Feuerbachs and Marxes were fools! It’s not for nothing that I.P. so diligently filters the entire second half of the 19th century - there’s a continuous diameter, and What that terrible dialectical materialism gave birth to?! -JC)Sorry for the reminder, but the author of these passages is like a scientist, even a Nobel Prize laureate, and not some pop or a journalist from the “about science” section of some utro.ru... Based on the letter with which “is written in the text” God" - you can guess the date of translation - 1986. (but we already lived under pluralism- and a couple of years have not passed since the release of the London edition of the masterpiece!)
...
Classical science was born of a culture permeated with the idea of a union between person halfway between the divine order and the natural order, and by god a rational and intelligible legislator, a sovereign architect whom we comprehend in our own image (that’s what classical science is! There’s no way in it without God - JC). She experienced a moment of cultural consonance, which allowed philosophers and theologians to deal with the problems of natural science, and scientists to decipher the creator's intentions and express opinions about the divine wisdom and power manifested in the creation of the world (it turns out that scientists are deciphering plans creator! -JC). With the support of religion and philosophy, scientists came to the conclusion that their activities were self-sufficient (yeah, especially with the support of religion! - JC), that it exhausts all the possibilities of a rational approach to natural phenomena...
Dualist implications of modern science... the description is objective to the extent that the observer is excluded from it, and the description itself is produced from a point lying de jure outside the world, that is, from the divine point of view, accessible from the very beginning to the human soul, created in the image of God... (a more clinically insane description of closed systems - we still need to look for that! - JC)
The Lord God, if he wished, could calculate trajectories in an unstable dynamic world. At the same time, he would get the same result that probability theory allows us to get (and we consider the theory of probability from a divine point of view! - I forgot what I wrote above? - JC). Of course, it would not be difficult for an omniscient god with his absolute knowledge to get rid of all chance. So, we can state that a close relationship between instability and probability undoubtedly exists." (brilliant argument! - JC)
...
We live in a dangerous and uncertain world, which does not inspire a sense of blind confidence, but only the same feeling of moderate hope that some Talmudic (sic! - JC) texts attribute to the god of the Book of Genesis"
- “Order from Chaos” - Ilya Prigogine, Isabella Stengers - the masterpiece ends with a quote from the “Book of Genesis” (why not from the Mahabharata?!).
Does anyone else doubt that What gave the Nobel Prize to this scientific digger, the Great Scientist? And in what wonderful and intelligible language this advanced (yes!) creation is written! You understand everything about cultural consonance And dualist implications?
By the way, according to the exact request " cultural consonance" - there are not a single result on Google. And if you want to find the source of the quote, you just need to type “moment of cultural consonance.”
Well, Prigogine himself indirectly admits in his autobiography that he was given a prize instead of other scientists who actually made amazing discoveries in the field that he hijacked - oh, you can’t take credit for the Belousov-Zhabotinsky reaction, as well as its interpretation. .. but the Nobel Prize for nonequilibrium thermodynamics was awarded to Prigozhin, and not to some lousy Soviet scientist (Belousov was also a red brigade commander!)
Scientific the pro-capitalist public, of course, was shocked when the reaction of the BZ in 1968 became known to the world - how is it that in the dark basements of Soviet torture laboratories they questioned the providence of God - they discovered self-oscillations - signs of self-organization - in chemical systems! Likewise, to justify the godless origin of life with its own reaction diamat they will cheat! This is where it came in handy promising methodologist, hereditary chemist, a boy from a good family, compiler of monographs on nonequilibrium statistical mechanics and cunning businessman-interpreter part-time - I. Prigozhin with an ideal profile - the son of refugees (difficult relationship with the new regime) from the bloody Bolsheviks! And he earned his fee in full.
Our vision of nature is undergoing radical changes towards multiplicity, temporality and complexity. For a long time, Western science was dominated by a mechanical picture of the universe. We now recognize that we live in a pluralistic world. There are phenomena that seem to us deterministic and reversible. Such, for example, are the movements of a pendulum without friction or the Earth around the Sun. But there are also irreversible processes that seem to carry the arrow of time. For example, if you merge two liquids such as alcohol and water, then from experience it is known that over time they will mix. The reverse process - spontaneous separation of the mixture into pure water and pure alcohol - is never observed. Therefore, mixing alcohol and water is an irreversible process. All chemistry, in essence, is an endless list of such irreversible processes.
It is clear that, in addition to deterministic processes, some fundamental phenomena, such as biological evolution or the evolution of human cultures, must contain some kind of probabilistic element. Even a scientist deeply convinced of the correctness of deterministic descriptions would hardly dare to assert that at the moment of the Big Bang, i.e. the origin of the Universe known to us, the date of publication of our book was inscribed on the tablets of the laws of nature. Classical physics viewed fundamental processes as deterministic and reversible. Processes associated with randomness or irreversibility were considered unfortunate exceptions to the general rule. Now we see how important a role irreversible processes and fluctuations play everywhere.
Although Western science has stimulated an unusually fruitful dialogue between man and nature, some of the consequences of the influence of natural science on human culture have not always been positive. For example, the opposition of the “two cultures” is largely due to the conflict between the timeless approach of classical science and the time-oriented approach that dominated the vast majority of the social sciences and humanities. But over the past decades, dramatic changes have occurred in natural science, as unexpected as the birth of geometry or the grandiose picture of the universe drawn in Newton’s “Mathematical Principles of Natural Philosophy.” We are increasingly aware that at all levels - from elementary particles to cosmology - randomness and irreversibility play an important role, the importance of which increases as our knowledge expands. Science is rediscovering time. Our book is dedicated to describing this conceptual revolution.
The revolution in question occurs at all levels: at the level of elementary particles, in cosmology, at the level of so-called macroscopic physics, covering the physics and chemistry of atoms or molecules, considered either individually or globally, as is done, for example, in the study liquids or gases. It is possible that it is at the macroscopic level that the conceptual revolution in natural science can be seen most clearly. Classical dynamics and modern chemistry are currently experiencing a period of radical change. If a few years ago we had asked a physicist what phenomena his science could explain and what problems remained open, he would probably have answered that we had not yet achieved an adequate understanding of elementary particles or cosmological evolution, but we had quite satisfactory knowledge of the processes occurring on scales intermediate between the submicroscopic and cosmological levels. Today, a minority of researchers, to which the authors of this book belong and which is growing every day, do not share such optimism: we are only beginning to understand the level of nature at which we live, and it is this level that our book focuses on.
To correctly assess the current conceptual re-equipment of physics, it is necessary to consider this process in the proper historical perspective. The history of science is by no means a linear development of a series of successive approximations to some deep truth. The history of science is replete with contradictions and unexpected turns. We devoted a significant part of our book to the scheme of the historical development of Western science, starting with Newton, i.e. from the events of three hundred years ago. We have sought to place the history of science within the history of thought in order to integrate it with the evolution of Western culture over the past three centuries. Only in this way can we truly appreciate the uniqueness of the moment in which we happen to live.
In the scientific heritage we have inherited, there are two fundamental questions to which our predecessors were unable to find an answer. One of them is the question of the relationship between chaos and order. The famous law of increasing entropy describes the world as constantly evolving from order to chaos. At the same time, as biological or social evolution shows, the complex arises from the simple. How can this be? How can structure emerge from chaos? We have now come quite far in answering this question. We now know that disequilibrium - the flow of matter or energy - can be a source of order.
But there is another, even more fundamental question. Classical or quantum physics describes the world as reversible, static. In their description there is no place for evolution either to order or to chaos. The information extracted from the dynamics remains constant over time. There is a clear contradiction between the static picture of dynamics and the evolutionary paradigm of thermodynamics. What is irreversibility? What is entropy? There are hardly any other issues that would be discussed so often in the development of science. Only now are we beginning to achieve that degree of understanding and that level of knowledge that allows us to answer these questions to one degree or another. Order and chaos are complex concepts. The units used in the static description given by dynamics are different from the units that were needed to create the evolutionary paradigm expressed by the growth of entropy. The transition from one unit to another leads to a new concept of matter. Matter becomes “active”: it gives rise to irreversible processes, and irreversible processes organize matter.<...>
What prerequisites of classical science have modern science managed to get rid of? Typically from those that were centered around the underlying thesis that at some level the world is simple and obeys time-reversible fundamental laws. Such a point of view seems to us today to be an oversimplification. To divide it means to become like those who see buildings as nothing more than piles of bricks. But from the same bricks you can build a factory building, a palace, and a temple. Only by considering the building as a whole do we gain the ability to perceive it as a product of an era, culture, society, style. There is another quite obvious problem: since the world around us has not been built by anyone, we are faced with the need to give a description of its smallest “bricks” (i.e., the microscopic structure of the world) that would explain the process of self-assembly.
The search for truth undertaken by classical science can itself serve as an excellent example of the duality that can be clearly seen throughout the history of Western European thought. Traditionally, only the unchanging world of ideas was considered, to use Plato's expression, “illuminated by the sun of the intelligible.” In the same sense, it was customary to see scientific rationality only in eternal and unchanging laws. Yet the temporary and transient were seen as an illusion. Nowadays such views are considered erroneous. We discovered that in nature, it is not the illusory, but the very real irreversibility that underlies most self-organization processes that plays a significant role. Reversibility and hard determinism in the world around us are applicable only in simple limiting cases. Irreversibility and randomness are now considered not as an exception, but as a general rule.<...>
Nowadays, the main focus of scientific research has shifted from substance to relationship, connection, time.
This dramatic change in perspective is not the result of an arbitrary decision. In physics, we are forced to do so by new, unforeseen discoveries. Who would have expected that many (if not all) elementary particles would be unstable? Who would have expected that with the experimental confirmation of the hypothesis of an expanding universe, we would have the opportunity to trace the history of the world around us as a single whole?
By the end of the 20th century. we have learned to better understand the meaning of two great revolutions in natural science, which had a decisive impact on the formation of modern physics: the creation of quantum mechanics and the theory of relativity. Both revolutions began with attempts to correct classical mechanics by introducing newly discovered universal constants into it. Now the situation has changed. Quantum mechanics has given us a theoretical basis for describing the endless transformations of one particle into another. Likewise, general relativity has become the foundation from which we can trace the thermal history of the Universe in its early stages.
By its nature, our Universe is pluralistic and complex. Structures can disappear, but they can also appear. Some processes, with the existing level of knowledge, can be described using deterministic equations, while others require the use of probabilistic considerations.
How can the apparent contradiction between the deterministic and the random be overcome? After all, we live in one world. As will be shown later, we are only now beginning to appreciate the significance of the entire range of problems associated with necessity and chance. In addition, we attach a completely different, and sometimes even opposite, meaning to the various phenomena we observe and describe than classical physics. We have already mentioned that according to the previously existing tradition, fundamental processes were considered to be deterministic and reversible, and processes that were in one way or another associated with randomness or irreversibility were interpreted as exceptions to the general rule. Nowadays we see everywhere how important the role played by irreversible processes and fluctuations is. The models considered by classical physics correspond, as we now understand, only to limiting situations. They can be created artificially by placing the system in a box and waiting until it reaches a state of equilibrium.
Artificial can be deterministic and reversible. The natural certainly contains elements of chance and irreversibility. This remark leads us to a new perspective on the role of matter in the Universe. Matter is no longer a passive substance described within the framework of a mechanistic picture of the world; it is also characterized by spontaneous activity. The difference between the new view of the world and the traditional one is so profound that, as already mentioned in the preface, we can rightfully talk about a new dialogue between man and nature.<...>
Two descendants of the theory of heat in a straight line - the science of converting energy from one form into another and the theory of heat engines - jointly led to the creation of the first "non-classical" science - thermodynamics. None of the contributions to the treasury of science made by thermodynamics can compare in novelty with the famous second law of thermodynamics, with the advent of which the “arrow of time” first entered physics. The introduction of one-way time was part of a broader movement in Western European thought. The 19th century can rightly be called the century of evolution: biology, geology and sociology began to be paid attention to in the 19th century. increasing attention to the study of the processes of emergence of new structural elements and increasing complexity. As for thermodynamics, it is based on the difference between two types of processes: reversible processes that do not depend on the direction of time, and irreversible processes that depend on the direction of time. We will get acquainted with examples of reversible and irreversible processes later. The concept of entropy was introduced to distinguish reversible processes from irreversible ones: entropy increases only as a result of irreversible processes.
Throughout the 19th century. the focus was on the study of the final state of thermodynamic evolution. Thermodynamics of the 19th century. was equilibrium thermodynamics. Nonequilibrium processes were viewed as minor details, disturbances, small insignificant details that did not deserve special study. Currently the situation has completely changed. We now know that far from equilibrium, new types of structures can spontaneously arise. Under highly nonequilibrium conditions, a transition from disorder, thermal chaos, to order can occur. New dynamic states of matter may arise, reflecting the interaction of a given system with the environment. We called these new structures dissipative structures, trying to emphasize the constructive role of dissipative processes in their formation.
Our book outlines some of the methods that have been developed in recent years to describe how dissipative structures arise and evolve. In presenting them, we will for the first time encounter such key words as “nonlinearity,” “instability,” and “fluctuation,” which run through the entire book as a leitmotif. This triad has begun to permeate our world views beyond physics and chemistry.
In discussing the contrast between the sciences and the humanities, we quoted the words of Isaiah Berlin. Berlin contrasted the specific and unique with the repetitive and general. A remarkable feature of the processes we are considering is that in the transition from equilibrium conditions to highly nonequilibrium ones, we move from the repeating and general to the unique and specific. Indeed, the laws of equilibrium are highly general: they are universal. As for the behavior of matter near the equilibrium state, it is characterized by “repetition”. At the same time, far from equilibrium, various mechanisms begin to operate, corresponding to the possibility of the emergence of dissipative structures of various types. For example, far from equilibrium, we can observe the emergence of a chemical clock - chemical reactions with a characteristic coherent (consistent) periodic change in the concentration of reagents. Far from equilibrium, self-organization processes are also observed, leading to the formation of inhomogeneous structures - nonequilibrium crystals.
It should be especially emphasized that this behavior of highly nonequilibrium systems is quite unexpected. Indeed, each of us intuitively imagines that a chemical reaction proceeds approximately as follows: molecules “float” in space, collide and, rearranging as a result of the collision, turn into new molecules. The chaotic behavior of molecules can be likened to the picture that atomists paint when they describe the movement of dust particles dancing in the air. But in the case of a chemical clock, we are faced with a chemical reaction that does not proceed at all as our intuition tells us. Simplifying the situation somewhat, we can say that in the case of a chemical clock, all molecules change their chemical identity simultaneously, at the correct intervals. If we imagine that the molecules of the starting substance and the reaction product are colored blue and red, respectively, then we would see how their color changes in the rhythm of the chemical clock.
It is clear that such a periodic reaction cannot be described based on intuitive ideas about the chaotic behavior of molecules. An order of a new, previously unknown type arose. In this case, it is appropriate to talk about new coherence, about the mechanism of “communication” between molecules. But a connection of this type can only arise under highly nonequilibrium conditions. It is interesting to note that such a connection is widespread in the living world. Its existence can be taken as the very basis of the definition of a biological system.
It should also be added that the type of dissipative structure largely depends on the conditions of its formation. External fields, such as the Earth's gravitational field or magnetic field, can play a significant role in the selection of the self-organization mechanism.
We are beginning to understand how, based on chemistry, it is possible to build complex structures, complex forms, including those that can become the precursors of living things. In highly nonequilibrium phenomena, a very important and unexpected property of matter has been reliably established: henceforth, physics can rightfully describe structures as forms of adaptation of a system to external conditions. We encounter a kind of mechanism of prebiological adaptation in the simplest chemical systems. In somewhat anthropomorphic language, we can say that in a state of equilibrium, matter is “blind,” while in highly disequilibrium conditions it acquires the ability to perceive differences in the external world (for example, weak gravitational and electric fields) and “take them into account” in its functioning.
Of course, the problem of the origin of life still remains very difficult, and we do not expect any simple solution in the near future. Nevertheless, with our approach, life ceases to resist the “ordinary” laws of physics, to fight against them in order to avoid the fate prepared for it - death. On the contrary, life appears to us as a unique manifestation of the very conditions in which our biosphere is located, including the nonlinearity of chemical reactions and highly nonequilibrium conditions imposed on the biosphere by solar radiation.
We discuss in detail the concepts that allow us to describe the formation of dissipative structures, for example, the concepts of bifurcation theory. It should be emphasized that significant fluctuations are observed in systems near bifurcation points. Such systems seem to “hesitate” before choosing one of several evolutionary paths, and the famous law of large numbers, if understood as usual, ceases to apply. A small fluctuation can initiate evolution in a completely new direction, which will dramatically change the entire behavior of the macroscopic system. An analogy with social phenomena and even with history inevitably arises. Far from the idea of contrasting randomness and necessity, we believe that both aspects play a significant role in the description of nonlinear, highly nonequilibrium systems.
To summarize, we can say that in the first two parts of our book we consider two opposing views of the physical world: the static approach of classical dynamics and the evolutionary view based on the use of the concept of entropy. Confrontation between such opposing approaches is inevitable. For a long time it was held back by the traditional view of irreversibility as an illusion, an approximation. Man introduced time into the timeless Universe. For us, such a solution to the problem of irreversibility is unacceptable, in which irreversibility is reduced to an illusion or is a consequence of certain approximations, since, as we now know, irreversibility can be a source of order, coherence, and organization.
The confrontation between the timeless approach of classical mechanics and the evolutionary approach became inevitable. The third part of our book is devoted to the acute clash of these two opposing approaches to describing the world. In it we examine in detail the traditional attempts to solve the problems of irreversibility, undertaken first in classical and then in quantum mechanics. The pioneering work of Boltzmann and Gibbs played a special role in this. Nevertheless, we can rightfully assert that the problem of irreversibility remains largely unresolved.<...>
Now we can judge with greater accuracy the origins of the concept of time in nature, and this circumstance leads to far-reaching consequences. Irreversibility is introduced into the macroscopic world by the second law of thermodynamics - the law of non-decreasing entropy. We now understand the second law of thermodynamics at the microscopic level. As will be shown later, the second law of thermodynamics functions as a selection rule - restrictions on the initial conditions that propagate at subsequent times according to the laws of dynamics. Thus, the second principle introduces a new, irreducible element into our description of nature. The second law of thermodynamics does not contradict dynamics, but cannot be derived from it.
Boltzmann already understood that there must be a close connection between probability and irreversibility. The distinction between past and future, and therefore irreversibility, can only enter into the description of a system if the system behaves in a sufficiently random manner. Our analysis confirms this point of view. Indeed, what is the arrow of time in the deterministic description of nature? What is its meaning? If the future is somehow contained in the present, which also contains the past, then what exactly does the arrow of time mean? The arrow of time is a manifestation of the fact that the future is not given, i.e. that, in the words of the French poet Paul Valéry, “time is a construction.”
Our daily life experience shows that there is a fundamental difference between time and space. We can move from one point in space to another, but we cannot turn back time. We cannot rearrange the past and the future. As we will see later, this feeling of the impossibility of reversing time now acquires a precise scientific meaning. Admissible (“allowed”) states are separated from states prohibited by the second law of thermodynamics, an infinitely high entropy barrier. There are many other barriers in physics. One of them is the speed of light. According to modern concepts, signals cannot travel faster than the speed of light. The existence of this barrier is very important: without it, causality would crumble to dust. Likewise, the entropy barrier is a prerequisite for giving a precise physical meaning to the connection. Imagine what would happen if our future became the past of some other people!<...>
But perhaps the most important progress is that the problem of structure, of order, now appears before us in a different perspective. As will be shown in Chap. 8, from the point of view of mechanics, classical or quantum, there cannot be evolution with unidirectional time. “Information” in the form that it can be defined in terms of dynamics remains constant over time. This sounds paradoxical. If we mix two liquids, then no “evolution” will occur, although it is not possible to separate them without resorting to the help of some external device. On the contrary, the law of non-decreasing entropy describes the mixing of two liquids as an evolution towards “chaos”, or “disorder”, the most probable state. Now we already have everything necessary to prove the mutual consistency of both descriptions: when talking about information or order, it is necessary to redefine the units we are considering each time. The important new fact is that we can now establish precise rules for the transition from units of one type to units of another type. In other words, we managed to obtain a microscopic formulation of the evolutionary paradigm expressed by the second law of thermodynamics. This conclusion seems important to us, since the evolutionary paradigm covers all of chemistry, as well as significant parts of biology and the social sciences. The truth has recently been revealed to us. The process of revision of basic concepts currently taking place in physics is still far from complete. Our goal is not at all to highlight the recognized achievements of science, its stable and reliably established results. We want to draw the reader's attention to new concepts born in the course of scientific activity, its prospects and new problems. We are clearly aware that we are only at the very beginning of a new stage of scientific research.<...>
We believe that we are on the way to a new synthesis, a new concept of nature. Perhaps one day we will be able to merge the Western tradition, which emphasizes experimentation and quantitative formulations, with a tradition such as the Chinese, with its ideas of a spontaneously changing, self-organizing world. At the beginning of the introduction, we cited the words of Jacques Monod about the loneliness of man in the Universe. The conclusion he comes to is:
“The ancient union [of man and nature] is destroyed. Man finally realizes his loneliness in the indifferent vastness of the Universe, from which he emerged by chance.”
Monod is apparently right. The ancient alliance is completely destroyed. But we see our purpose not in mourning the past, but in trying to find a guiding thread leading to some unified picture of the world in the extraordinary diversity of modern natural sciences. Each great period in the history of natural science leads to its own model of nature. For classical science, such a model was a clock, for the 19th century - the period of the industrial revolution - a steam engine. What will become a symbol for us? Our ideal seems to be most fully expressed by sculpture - from the art of Ancient India or Central America of the pre-Columbian era to modern art. In some of the most perfect examples of sculpture, for example, in the figure of the dancing Shiva or in miniature models of the temples of Guerrero, one can clearly sense the search for an elusive transition from rest to movement, from stopped time to flowing time. We are convinced that it is this confrontation that determines the unique identity of our time.<...>
By connecting entropy with a dynamic system, we thereby return to Boltzmann's concept: probability reaches a maximum in a state of equilibrium. The structural units that we use to describe thermodynamic evolution behave chaotically in a state of equilibrium. In contrast, under weakly nonequilibrium conditions, correlations and coherence arise.
Here we come to one of our main conclusions: at all levels, be it the level of macroscopic physics, the level of fluctuations or the microscopic level, the source of order is disequilibrium. Disequilibrium is what creates “order out of chaos.” But, as we already mentioned, the concept of order (or disorder) is more complex than one might think. Only in extreme cases, for example in rarefied gases, does it acquire a simple meaning in accordance with the pioneering works of Boltzmann.<...>
Now our confidence in the “rationality” of nature has been shaken, partly as a result of the rapid growth of natural science in our time. As noted in the Preface, our vision of nature has undergone fundamental changes. We now take into account aspects of change such as multiplicity, time dependence and complexity. Some of the shifts that have occurred in our views of the world are described in this book.
We were looking for general, comprehensive schemes that could be described in the language of eternal laws, but we discovered time, events, particles undergoing various transformations. While searching for symmetry, we were surprised to discover processes accompanied by symmetry breaking at all levels - from elementary particles to biology and ecology. We have described in our book the clash between dynamics, with its inherent symmetry in time, and thermodynamics, which is characterized by a one-way direction of time.
A new unity is emerging before our eyes: irreversibility is the source of order at all levels. Irreversibility is the mechanism that creates order out of chaos.
Prigogine I., Stengers I. Order out of chaos. A new dialogue between man and nature. M., 1986. P. 34-37, 47-50, 53-61, 65-66, 357, 363.
Loading...