In the picture of classical mechanics, time is reversible, and there is no fundamental difference between events that occur in the past and in the future. But nearly 50 years ago, the Nobel prize-winning physico-chemist Prigogine introduced irreversibility and the arrow of time into classical thermodynamics, expanding our understanding of thermodynamics: irreversible processes can not only disrupt order and increase the entropy of the universe, but can also create highly ordered complex structures and life itself.
In 2017, on the occasion of prigogine's 100th birthday, Chaos, an interdisciplinary journal of nonlinear science owned by the American Physical Society (AIP), published a commemorative article reviewing Prigogine's academic contributions at different times and the "poet of thermodynamics" with other scientists.
撰文 | Dilip Kondepudi，Tomio Petrosky，John A. Pojman
Translate | Zhang Ao
Review | Liang Jin
Original link: https://aip.scitation.org/doi/full/10.1063/1.5008858
1. Poet of thermodynamics
Friends and colleagues familiar with Ilya Prigogine called him a "poet of thermodynamics," which is an apt description. When Prigozin talks about thermodynamics and irreversible processes, it feels like he understands more than his language conveys. It is true that natural processes around us are irreversible. Irreversible processes not only increase the entropy of the universe and disrupt order, but can also accomplish the opposite: the creation of highly ordered complex structures and life itself.
Prigogine believes that this is a profound aspect that thermodynamics reveals to nature. When he saw the famous South Indian sculpture Nataraja (Dancing Shiva depicting a cosmic dance that perfectly balances creation and destruction), he made sure to have a highly artistically valuable bronze statue of Nataraja in his art collection. A photograph of the statue became the cover of his book Thermodynamic Theory of Structure Stability and Fluctuations, which he co-authored with Paul Glansdorff. It is the psalm of thermodynamics, the creation and destruction that emerges from the same source, the dance of the universe in perfect balance. One can infer all this from Prigozin's treatise on thermodynamics.
Figure 1. Shiva dancing on the cover of Thermodynamic Theory of Structure Stability and Fluctuations
Dissipative structures were named nearly 50 years ago by Prigogine for complex structures resulting from irreversible processes. As stated in this article celebrating the centenary of his birth (Prigorjin was born January 25, 1917), the study of dissipative structures remains a very active subject, constantly advancing into new areas. If we continue to study, we may gain deeper insights and may even discover new laws or theorems to better understand how complex structures spontaneously form, their responses to changes in physical parameters, and their collective behavior. These advances in other fields are also our search for a thermodynamic understanding of biological processes, even those that create life.
Prigogine was convinced of the centrality of irreversible processes in nature and the veracity of the arrow of time, but he had to confront the vexing duality of physics. From the classical mechanical point of view of the reversibility of time, there is no fundamental difference between the movements that occur in the future or in the past (and all the transformations of matter). Therefore, many people think that the irreversible process and the arrow of time cannot be real, but only an illusion, an illusion created by our limited ability. Prigozin is extremely opposed to this view of irreversible processes and the arrow of time. Many times we see him say with passion and certainty in speeches and café conversations: "Irreversible processes create us, but we don't create them." At times, his formulation is more literary: "We are the children of the arrow of time, the arrow of evolution, not its ancestors." ”
In order to adapt to the reality of irreversible processes and the arrow of time, classical mechanics must be modified or expanded. To this end, he promoted the development of the theory of non-unitary transformation. In his concluding remarks to the 1977 Nobel Lecture[2], he pointed out: "The introduction of thermodynamic irreversibility through the theory of non-unitary positive transformations profoundly changed the dynamic structure. We go from groups to semi-groups, from trajectories to processes. This evolution is consistent with some of the major changes we describe in the material world this century. This theory continues to evolve to this day.
Prigogine's scientific contributions can be roughly divided into three periods: (i) in the early days, he reclassified thermodynamics as the science of irreversible processes, changing the state that thermodynamics was about states in the 19th century; (ii) during the Brussels-Austin group, constructing the theory of dissipative structures and extensively studying different systems; and (iii) late, his group focused on expanding the formulation of classical mechanics, making irreversibility the basis of physics.
2. Thermodynamic theory of processes
In the first phase of his work, Prigozin synthesized concepts developed by his mentor Theophile DeDonder and Duhem, Natanson, Jaumann, Onsager, and others, radically changing the formulation of thermodynamics to make it a theory of processes rather than a theory of states.
As it was elaborated in the 19th century, thermodynamics identified two basic functions of the state—energy and entropy, the former related to the first law of thermodynamics and the latter to the second law of thermodynamics. In this classical theory of thermodynamics, only an ideal, infinitely slow reversible process can calculate a change in entropy, i.e. dS = dQ/T; there is no formula that can relate the change in entropy to an irreversible and non-zero rate of actual processes in nature. For irreversible processes, the theory only states that dS > dQ/T, which excludes irreversible processes. But the theory is still very powerful, because we can use the concept of reversible processes to calculate the difference in entropy between two states. In addition, since the calculation of entropy changes is limited to infinitely slow reversible processes, classical thermodynamics cannot calculate the rate of change of entropy (dS/dt) or relate the rate of change of entropy to irreversible processes.
*The state function is a function that describes the macroscopic quantities (such as temperature, entropy, pressure, volume, energy, etc.) in which the thermodynamic system is located. In a thermodynamic system in equilibrium, each macroscopic quantity has a definite value and is determined only by the state in which the system is located, independent of the process of reaching equilibrium.
Bridgman described the state of classical thermodynamics in the 19th century in his 1943 monograph The Nature of Thermodynamics[3]: "It is almost always emphasized that thermodynamics is concerned with reversible processes and equilibrium states, which are independent of irreversible processes or systems far from equilibrium, in which change takes place at a limited rate. Considering that temperature itself is defined in terms of equilibrium states, the importance of equilibrium states is obvious. But acknowledging the impotence of thermodynamics in the face of irreversible processes seems surprising. Physicists don't usually adopt this defeatist attitude. ”
Following the progress of Lars Onsager in the 1930s, Prigozin introduced the thermodynamic theory of irreversible processes. The key concept of this theory is local equilibrium, which assumes that the system is in equilibrium within the unit volume at each location. Thus, temperature and other state variables become functions of position, and the system as a whole is uneven. The concept of local equilibrium is supported by statistical physics. Statistical physics shows that within the local range, particle velocities quickly reach the Maxwell rate distribution, allowing the concept of temperature to be clearly defined at each location. Prigogine's thermodynamic theory defines the variation of entropy in a system at dt intervals dS follows
This article provides an overview of Prigogine's main contributions in each of the three periods. The following is related to the contribution of the first period. Prigogine and De Decker's article "Stochastic Approach to irreversible thermodynamics"[7] shows how thermodynamic formulas can be extended to explicitly include macroscopic observable fluctuations. In this review, the authors propose a mathematical formulation that links fluctuations, irreversibility, and the contribution of fluctuations to entropy.
In an article titled "The underdamped Brownian duet and stochastic linear irreversible thermodynamics",[8] Proesmans and Van den Broeck discuss key features of stochastic thermodynamics, such as the fluctuation theorem, fluctuation-dissipation relationships, and efficiency at fluctuations. The article discusses a concrete example of a Brown particle driven by a periodic force.
Malek-Mansour and Baras critically commented on the fluctuation theorem through an article titled "Fluctuation theorem: A critical review".[9] The theorem has many subtle features that unfortunately lead to the emergence of a number of articles claiming to violate the second law of thermodynamics. Quoting Max Planck, the author rightly reminds the reader that the second law of thermodynamics is a macroscopic law that indicates the impossibility of a second type of perpetual motion machine, which is either valid in all systems or invalid in all systems, and there is no third possibility. This article points out several aspects that need to be carefully considered when applying the fluctuation theorem.
3. Widespread dissipative structures
Under Prigogine's leadership, the active Brussels School of Thermodynamics and Statistical Mechanics flourished, publishing highly successful monographs[10-12] and translating them into several languages. Today, stimulated by nanotechnology and other technologies, thermodynamics is producing new developments.
In the late 1950s and early 1960s, a new phase of activity began with the recognition that non-equilibrium conditions could produce chemical oscillations. It stems from the recognition that irreversible processes can drive the system into an organized state when it moves away from the thermodynamic equilibrium; the phenomenon of self-organization begins to be recognized. Irreversible processes produce entropy that are thought to represent disorder, however, the same irreversible processes also produce self-organization, from which the study of dissipative structures arises. This is the key to understanding the origins of order and the diverse forms and functions we see in nature. This also raises new questions about the stability of non-equilibrium states, the discovery of nonlinearities in the equations of systems that describe systems far from thermodynamic equilibrium, and the discovery of many self-organizing systems.
In 1967, when Prigozin accepted the position of director of the Center for The Study of Statistical Mechanics and Thermodynamics at the University of Texas in Austin, his team expanded to become the Brussels-Austin team. The study of dissipative structures has entered a new phase, attracting researchers from all over the world. For this reason, the Nobel Prize in Chemistry was awarded to Prigozin in 1977 in recognition of his contributions to thermodynamics. His book, co-authored with Grégoire Nicolis, summarized much of the work on dissipative structures of the time and was also published in the same year. A few years later, in his new book Order out of Chaos,[14] Prigotjin gave a broader description of time, complexity, and irreversible processes. The book was translated into 18 languages and was widely circulated. Subsequently, Prigozin wrote several books on the arrow of time and complexity for the general reader. Dissipative structure research remains a thriving field of research.
The article on dissipative structures is the main part of this article. Albert Goldbete is well known for his contributions to the field of biochemical oscillations, and he makes an exciting and brilliant review in his article "Dissipative Structures and Biological Rhythms".[15] A table in this paper (see Table 1) shows the astonishing presence of periodicity at the cellular and supercellular levels.
Table 1. The main biorhythms that occur at all levels of biological tissues increase from top to bottom, with cycle lengths varying by more than 10 orders of magnitude | Source: Goldbeter, Albert. “Dissipative structures and biological rhythms.” Chaos (Woodbury, N.Y.) vol. 27,10 (2017): 104612. doi:10.1063/1.4990783
In the same field, Amemiya et al. wrote an article titled "Primordial Oscillations in Life: Direct Observation of Glycolytic Oscillations in Individual HeLa Cervical Cancer Cells".[16] The role of glycolytic oscillations in cell rhythms and cancer cells was discovered and outlined. The authors also discuss self-assembly and its relationship to dissipative structures: dissipative structures and self-assembling complement each other.
Kondepudi, Kay, and Dixon, et al., discuss the relevance of dissipative structures in understanding organisms in understanding organisms in "Dissipative structures, machines, and organisms: A perspective".[17] The authors propose a voltage-driven system capable of exhibiting phenomena similar to what we see in organisms. They show that almost all of the different aspects of complex behavior observed in the system can be described as an evolution of a state toward a higher rate of entropy generation. You can also find ideas about the fundamental difference between machines and organisms in this article.
One of the most famous aspects of dissipative structures is explaining how speckles form in chemical systems far from equilibrium. In their article entitled "Dissipative Structures: From Reaction-Diffusion to Chemo-Hydrodynamic Patterns",[18] Burdoni and De Wit discuss how the interaction between reactions and diffusions produces local spatiotemporal maps when different reactants come into contact with each other. Using the Brusselator model (see Figure 2), they found local waves, Turing specks, and reaction-diffusion specks.
Figure 2. Originally proposed by Prigozin and his colleagues, the Brussels oscillator model is a set of nonlinear differential equations that model autocatalytic reactions. Here's a Brussels oscillator simulation of a reaction-diffusion system in two-dimensional space. | Source: Wikipedia
In the article "Chlorine dioxide-induced and Congo red-inhibited Marangoni effect on the chlorite-trithionate reaction front", Liu The effect of Malengol convection on the chlorite-trisulfate reaction interface was studied. Chlorine dioxide produced during the reaction changes the surface tension, causing the liquid to flow. However, the addition of Congo red creates a oscillating interface, and bromophenol blue produces multiple vortices.
*The Marengoni effect refers to the presence of a surface tension gradient at the fluid interface, the surface tension of the liquid with strong surface tension is greater than the tensile force of the liquid with weak surface tension on the surrounding liquid, resulting in the penetration of the liquid with weak surface tension to the strong side. The Italian physicist Carlo Marangoni first studied this phenomenon in an 1865 paper.
Biria et al. reviewed light waves in light-reactive systems, and their article "Coupling nonlinear optical waves to photoreactive and phase-separating soft matter: Current status and perspectives" [20], How nonlinear optical dynamics can be coupled separately from phases to create spot formations with practical uses are discussed.
Viner et al. studied the effect of rotational acceleration on mixed-phase droplet dissolution in the article "Effect of pseudo-gravitational acceleration on the dissolution rate of miscible drops"[21], in which the rotational acceleration in a rotating droplet tension meter creates a pseudo-gravitational field. This in turn creates a force that hinders dissolution (air pressure diffusion), but also creates a buoyancy-driven flow to promote dissolution.
Bunton et al.'s article "The effect of a crosslinking chemical reaction on pattern formation in viscous fingering of miscible fluids in a Hele–Shaw cell*"[22], The effect of crosslinking of thiols and acrylates on the formation of the hele-Shaw box mixed-phase fluid viscosity finger map was studied, and they found that the plaque map could be changed by adjusting the reaction rate.
Figure 3. The Hele-Shaw box consists of a pair of parallel plates with a tiny gap in the middle, named after Henry Selby Hele-Shaw, who studied the problem in 1898. Its importance is reflected in the fact that the Hele-Shaw flow is a good approximation of various problems in fluid mechanics. | Source: Wikipedia
By the time Prigozin won the Nobel Prize in Chemistry at the age of 60, he had already begun to think about how to modify mechanics to incorporate irreversibility and the arrow of time, thus beginning the third phase of his research. But the problem bothered many people before him, including people like Henri Poincaré, and it touched on the core of the powertrain.
Poincaré's division of dynamical systems into integrable and non-accumulatable systems was an important source of Prigogine's thought. Poincaré proved that in non-accumulative systems , it is not possible to construct a regular or unitary positive transformation by acting on the corresponding unturbed invariants to produce new motion invariants. Prigozin saw a link between this result and irreversibility. In addition, "chaotic systems" show that dynamics is not a science that allows us to predict future behavior indefinitely, and Prigozin sees the limitations of classical mechanics and finds that probability and irreversibility must be used as the basis for expanding classical mechanics. To this end, he and his collaborators began to construct a theory of non-unitary transformations in which probabilities arise not because we cannot determine microstates, but because of the dynamics of resonance singularities in non-product systems. He studied the theory until his death in 2003. Today, the theory continues to evolve.
4. Beyond dynamics
The third phase of Prigogine's scientific contribution analyzes the irreversible processes of the Hamiltonian system with an infinite number of degrees of freedom in open dynamical systems and analyzes nonlinear processes in chaotic systems and quantum optics.
Petrosky et al.'s "Microscopic description of irreversibility in quantum Lorentz gas by complex spectral analysis of the Liouvillian outside the Hilbert space" (Microscopic description of the irreversibility of quantum Lorentz gases by composite spectral analysis of The Liu weir function outside Hilbert space)[23], discusses the application of the composite spectral analysis of the Liu Weir function. Prigozin and his Brussels-Austin group developed this type of analysis. For quantum Lorentz gases, they demonstrated that the irreversible processes of the Hamiltonian system are obtained on a purely kinetic basis at all spatial and temporal scales, including the range of microscopic atomic interactions, without relying on any solipsistic operation.
Ordonez and Hatano's article "Irreversibility and the breaking of resonance-antiresonance symmetry"[24], using a simple model of one unit point coupled to two leads in a lattice point, proposes an interesting unit decomposition of time-reversed symmetry, using a simple model of a unit point coupled to two leads in a lattice point. to describe the irreversible processes of open quantum systems. The results show that this unit decomposition contains both resonant states that will decay in the future and anti-resonance states that will decay in the past; a time-reversed invariant state contains both equally weighted resonant and anti-resonant components, but as the system evolves, this symmetry will automatically break.
Fathi et al.'s article "A wave-function model for the CP-violation in mesons" [25] discusses CP symmetry breaking in mesons using the binary Friedrichs Hamilton model. The Friedrichs model has been one of the prototype models analyzed by Prigozin and his colleagues. The model describes the dynamic roots of irreversibility, where irreversibility arises from the resonance singularity that arises in the solution of the fundamental equation of motion symmetrical to the direction of time.
Hasegawa et al.'s article "Generalized second law for a simple chaotic system"[26] discusses the generalization of the second law of thermodynamics (nonequilibrium maximum work formulation) in a simple chaotic system. They showed that even for a Gibbs-Shannon entropy conservation system, thermodynamic entropy increased.
Barr et al.'s article "Signatures of Chaos in the Brillouin zone",[27] also discusses the chaotic behavior of quantum billiard balls laid on an infinite plane. They show that when the classical dynamic behavior of billiards changes from order to chaos, the energy bands in Brillouin begin to mix.
Finally, Vanbever et al.'s article "Semiconductor surface emitting lasers for photon pairs generation" discusses nonlinear processes in quantum optics. This nonlinear process has always been one of Prigogzu's favorite subjects. They investigated the feasibility of generating photon pairs in a Resonant Vertical Cavity Surface-Emitting Laser (VCSEL) through third-order nonlinear and four-wave mixing interactions.
We remember Prigogine not only for being a dynamic and inspiring colleague, but also for being a very kind and generous person. He enjoys socializing with people and often has dinner with colleagues. Throughout his life, he welcomed visitors and gave them generous support. He is an avid art collector with museum-level pre-Columbian art. In his youth, he was also an accomplished keyboard musician. His epitaph reads:
THE BARREL IS A SOURCE OF CR ATIVIT
(Surprise is the source of creativity)
Commemorative review
Prigozin is Dilip Kondepudi's phD supervisor. Kondepudi continued to work with Prigogine for many years after earning his Doctorate, and together they published many articles. In 1998, they co-authored a textbook titled Modern Thermodynamics: From Heat Engines to Dissipative Structures, which was published in 25 countries in six languages. Kondepudi shared with us a precious memory related to Prigogine:
When I was at the University of Texas in Austin, several times Prigozin came to my office, habitually tapped his chest with his left hand and said, "Dilip, let's go have some coffee... If you can. "I think it means he wants to get out of the office and sort out some of the thoughts in his head. I enjoyed those informal discussions with him. I had the opportunity to witness his process of forming an idea through discussion, to get his opinion on an idea I was thinking about, and to ask him to explain something he had said in a recent speech that I didn't understand. We often went to a small bakery near the university with a long name called "aptain Quackenbush's Intergalactic Dessert Company and Espresso Café" We sat there with a cup of fine European coffee, and he often talked about the need for physics to change and incorporate irreversibility into the basic principles. I can still hear him in my head: "It's amazing that people believe that time is reversible." "I deliberately took my book and pen with me and went to the coffee room to chat. One day, he wrote a paper that combined general relativity and thermodynamics to make irreversibility a fundamental principle. I saw a grand plan in it, so I left the piece of paper, which is now preserved in prigogine's souvenir book.
Tomio Petrosky met Prigozin in 1980 and worked closely with him. In the final stages of Prigogine's life, Tomio Petrosky was one of his closest colleagues. They wrote many papers together and often went to the bakery kondepudi mentioned above, where they talked with Prigozin about various topics. He recalled:
Occasionally, we hear Prigogzu's wise words. He said: "There are two most important things in my life. One is encountering people. The other was a discussion with my colleagues. If you don't discuss, you can only get the results you expected. At a press conference in Japan, Prigotsu was asked what motivated and motivated his scientific work. He replied, "It's dissatisfaction!" It seems to me that many scientists are satisfied with the current explanations of the fundamental laws of physics, especially those relating to time. I think there are some things that are not satisfactory. Eliminating this dissatisfaction is a powerful motivator for me to continue my scientific research. ”
John Pojman was a graduate student at the University of Texas at Austin from 1984 to 1988. He recalls how Prigogine influenced his career:
During my senior year at Georgetown University, I became interested in chemical self-organization. I visited Professor Joseph Earley, who demonstrated the Belousov-Zhabotinsky reaction in my general chemistry class three years ago* and said I should go to graduate school at the University of Texas at Austin and work with Professor Prigogine. In the spring of 1984, I applied to the University of Texas and visited the University of Austin. I wrote a letter to Professor Prigozin and had a meeting with him. He waited for me in the lobby of the apartment building in slippers and invited me to his apartment. He said very kindly, "I have half an hour, what do you want to talk about?" I don't remember what I answered, but he went on to speak on the arrow of time and how empires have fallen and risen. I was mesmerized by his train of thought and eventually got into the University of Texas, where I worked on chemistry with Professor Prigozin and Professor James Whitesell. During Prigogine's visit to Texas, I met him twice a year and he would continue to spark my interest in self-organization. Although my supervisor was actually Dilip Kondepudi, who was a postdoc at the time, Professor Prigozin had been supporting me in my research on Maxwell-Boltzmann gas for polymer exchange reactions.
bibliography
[1] P. Glansdorff and I. Prigogine, Thermodynamic Theory of Structure, Stability and Fluctuations ( John Wiley Sons, New York, 1971), Translations in French, Russian and Japanese.
[2] “Ilya Prigogine - Nobel Lecture: Time, Structure and Fluctuations,” Nobelprize.org. Nobel Media AB 2014.
[3] P. W. Bridgman, The Nature of Thermodynamics ( Harvard University Press, Cambridge, MA, 1943), p. 133.
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[28] L. R. Vanbever, E. Karpov, and K. Panajotov, Chaos 27, 104613 (2017).
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