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非平衡热力学的极值定理

2021-02-19T04:42:33Z

Yetmings：

此词条由Solitude初步翻译。

{{Essay|date=December 2010}}

'''Energy dissipation and entropy production extremal principles''' are ideas developed within [[non-equilibrium thermodynamics]] that attempt to predict the likely steady states and dynamical structures that a physical system might show. The search for extremum principles for non-equilibrium thermodynamics follows their successful use in other branches of physics.<ref name="Onsager 1931 I">{{cite journal | last1 = Onsager | first1 = L | year = 1931 | title = Reciprocal relations in irreversible processes, I | url = | journal = Physical Review | volume = 37 | issue = 4| pages = 405–426 | doi=10.1103/physrev.37.405| bibcode = 1931PhRv...37..405O| doi-access = free }}</ref><ref name="Gyarmati 1970"/><ref name="Ziegler 1983">Ziegler, H., (1983). ''An Introduction to Thermomechanics'', North-Holland, Amsterdam, {{ISBN|0-444-86503-9}}</ref><ref name="M&S 2006">{{cite journal | last1 = Martyushev | first1 = L.M. | last2 = Seleznev | first2 = V.D. | year = 2006 | title = Maximum entropy production principle in physics, chemistry and biology | url = http://www.rsbs.anu.edu.au/ResearchGroups/EBG/profiles/Roderick_Dewar/Martyushev%20and%20Seleznev%202006%20Phys%20Rep.pdf | journal = Physics Reports | volume = 426 | issue = 1 | pages = 1–45 | doi = 10.1016/j.physrep.2005.12.001 | bibcode = 2006PhR...426....1M | access-date = 2009-10-10 | archive-url = https://web.archive.org/web/20110302120848/http://www.rsbs.anu.edu.au/ResearchGroups/EBG/profiles/Roderick_Dewar/Martyushev%20and%20Seleznev%202006%20Phys%20Rep.pdf | archive-date = 2011-03-02 | url-status = dead }}</ref><ref name="MNS 2007">{{cite journal | last1 = Martyushev | first1 = I.M. | last2 = Nazarova | first2 = A.S. | last3 = Seleznev | first3 = V.D. | year = 2007 | title = On the problem of the minimum entropy production in the nonequilibrium stationary state | url = | journal = Journal of Physics A: Mathematical and Theoretical | volume = 40 | issue = 3| pages = 371–380 | doi=10.1088/1751-8113/40/3/002| bibcode = 2007JPhA...40..371M }}</ref><ref name="Hillert Agren 2006">{{cite journal | last1 = Hillert | first1 = M. | last2 = Agren | first2 = J. | year = 2006 | title = Extremum principles for irreversible processes | url = | journal = Acta Materialia | volume = 54 | issue = 8| pages = 2063–2066 | doi=10.1016/j.actamat.2005.12.033}}</ref> According to Kondepudi (2008),<ref>Kondepudi, D. (2008)., ''Introduction to Modern Thermodynamics'', Wiley, Chichester UK, {{ISBN|978-0-470-01598-8}}, page 172.</ref> and to Grandy (2008),<ref name="Grandy 2008">Grandy, W.T., Jr (2008). ''Entropy and the Time Evolution of Macroscopic Systems'', Oxford University Press, Oxford, {{ISBN|978-0-19-954617-6}}.</ref> there is no general rule that provides an extremum principle that governs the evolution of a far-from-equilibrium system to a steady state. According to Glansdorff and Prigogine (1971, page 16),<ref name="G&P 1971"/> irreversible processes usually are not governed by global extremal principles because description of their evolution requires differential equations which are not self-adjoint, but local extremal principles can be used for local solutions. Lebon Jou and Casas-Vásquez (2008)<ref name="Lebon Jou Casas-Vázquez 2008">Lebon, G., Jou, J., Casas-Vásquez (2008). ''Understanding Non-equilibrium Thermodynamics. Foundations, Applications, Frontiers'', Springer, Berlin, {{ISBN|978-3-540-74251-7}}.</ref> state that "In non-equilibrium ... it is generally not possible to construct thermodynamic potentials depending on the whole set of variables". Šilhavý (1997)<ref name="Continuous Media page 209">Šilhavý, M. (1997). ''The Mechanics and Thermodynamics of Continuous Media'', Springer, Berlin, {{ISBN|3-540-58378-5}}, page 209.</ref> offers the opinion that "... the extremum principles of thermodynamics ... do not have any counterpart for [non-equilibrium] steady states (despite many claims in the literature)." It follows that any general extremal principle for a non-equilibrium problem will need to refer in some detail to the constraints that are specific for the structure of the system considered in the problem.

Energy dissipation and entropy production extremal principles are ideas developed within non-equilibrium thermodynamics that attempt to predict the likely steady states and dynamical structures that a physical system might show. The search for extremum principles for non-equilibrium thermodynamics follows their successful use in other branches of physics. According to Kondepudi (2008), and to Grandy (2008), there is no general rule that provides an extremum principle that governs the evolution of a far-from-equilibrium system to a steady state. According to Glansdorff and Prigogine (1971, page 16), state that "In non-equilibrium ... it is generally not possible to construct thermodynamic potentials depending on the whole set of variables". Šilhavý (1997) offers the opinion that "... the extremum principles of thermodynamics ... do not have any counterpart for [non-equilibrium] steady states (despite many claims in the literature)." It follows that any general extremal principle for a non-equilibrium problem will need to refer in some detail to the constraints that are specific for the structure of the system considered in the problem.

能量耗散和产生熵极值原理是在非平衡热力学中发展起来的概念，它们试图预测物理系统可能表现出的稳态和动态结构。在物理学的其他分支成功应用极值原理之后，我们对非平衡态热力学的极值原理进行了探索。根据孔德普迪 Kondepudi (2008年)和格兰迪Grandy (2008年)的说法，没有一个一般规则可以提供一个极值原理来管理一个远离平衡的系统向稳定状态的演化。根据格兰斯多夫Glansdorff和普里戈金Prigogine(1971年，第16页) 的说法，“在非平衡状态下... ... 通常不可能根据整个变量集来构造热力学势”。希尔哈维Šilhavý(1997)认为“ ... 热力学的极值原理... 对于非平衡稳态没有任何对应的原理（尽管文献中有许多说法)。”由此可见，针对非平衡问题的任何一般极限原理都需要在某些细节上参考问题中所考虑的系统结构所特有的制约因素。

==Fluctuations, entropy, 'thermodynamics forces', and reproducible dynamical structure==

波动，熵，“热力学力”和可重现的动力学结构

Apparent 'fluctuations', which appear to arise when initial conditions are inexactly specified, are the drivers of the formation of non-equilibrium dynamical structures. There is no special force of nature involved in the generation of such fluctuations. Exact specification of initial conditions would require statements of the positions and velocities of all particles in the system, obviously not a remotely practical possibility for a macroscopic system. This is the nature of thermodynamic fluctuations. They cannot be predicted in particular by the scientist, but they are determined by the laws of nature and they are the singular causes of the natural development of dynamical structure.<ref name="G&P 1971"/>

Apparent 'fluctuations', which appear to arise when initial conditions are inexactly specified, are the drivers of the formation of non-equilibrium dynamical structures. There is no special force of nature involved in the generation of such fluctuations. Exact specification of initial conditions would require statements of the positions and velocities of all particles in the system, obviously not a remotely practical possibility for a macroscopic system. This is the nature of thermodynamic fluctuations. They cannot be predicted in particular by the scientist, but they are determined by the laws of nature and they are the singular causes of the natural development of dynamical structure.

表面的 "波动 "是在初始条件不精确时出现的，是形成非平衡动力结构的动力。这种波动的产生并不涉及任何特殊的自然力量。初始条件的精确规定需要陈述系统中所有粒子的位置和速度，这对于宏观系统来说显然不是一个遥不可及的实际可能性。这就是热力学波动的本质。科学家无法特别预测它们，但它们是由自然规律决定的，它们是动态结构自然发展的独特原因。

It is pointed out<ref>Grandy, W.T., Jr (2004). Time evolution in macroscopic systems. I: Equations of motion. ''Found. Phys.'' '''34''': 1-20. See [http://physics.uwyo.edu/~tgrandy/evolve.html].</ref><ref>Grandy, W.T., Jr (2004). Time evolution in macroscopic systems. II: The entropy. ''Found. Phys.'' '''34''': 21-57. See [http://physics.uwyo.edu/~tgrandy/entropy.html].</ref><ref>Grandy, W.T., Jr (2004). Time evolution in macroscopic systems. III: Selected applications. ''Found. Phys.'' '''34''': 771-813. See [http://physics.uwyo.edu/~tgrandy/applications.html].</ref><ref>Grandy 2004 see also [http://physics.uwyo.edu/~tgrandy/Statistical_Mechanics.html].</ref> by W.T. Grandy Jr that entropy, though it may be defined for a non-equilibrium system, is when strictly considered, only a macroscopic quantity that refers to the whole system, and is not a dynamical variable and in general does not act as a local potential that describes local physical forces. Under special circumstances, however, one can metaphorically think as if the thermal variables behaved like local physical forces. The approximation that constitutes classical irreversible thermodynamics is built on this metaphoric thinking.

It is pointed out by W.T. Grandy Jr that entropy, though it may be defined for a non-equilibrium system, is when strictly considered, only a macroscopic quantity that refers to the whole system, and is not a dynamical variable and in general does not act as a local potential that describes local physical forces. Under special circumstances, however, one can metaphorically think as if the thermal variables behaved like local physical forces. The approximation that constitutes classical irreversible thermodynamics is built on this metaphoric thinking.

W.T.格兰迪(W.T. Grandy Jr) 指出，熵虽然可以为非平衡系统定义，但严格考虑时，它只是一个宏观的量，指的是整个系统，并不是一个动态变量，一般情况下，它并不能作为描述局部物理力的局部势。但在特殊情况下，我们可以比喻为热变量的行为就像局部物理力一样。构成经典不可逆热力学的近似就是建立在这种隐喻思维的基础上。

As indicated by the " " marks of Onsager (1931),<ref name="Onsager 1931 I"/> such a metaphorical but not categorically mechanical force, the thermal "force", <math>X_{th}</math>, 'drives' the conduction of heat. For this so-called "thermodynamic force", we can write

正如昂萨格Onsager(1931)的" "双引号标记所表明的那样，<ref name="Onsager 1931 I"/>这样一个比喻性的但不是绝对的机械力，即热 "力"， <math>X_{th}</math>，"驱动 "着热量的传导。对于这个所谓的 "热力"，我们可以写为

:::::<math>X_{th} = - \frac{1}{T} \nabla T</math>.

Actually this thermal "thermodynamic force" is a manifestation of the degree of inexact specification of the microscopic initial conditions for the system, expressed in the thermodynamic variable known as temperature, <math>T</math>. Temperature is only one example, and all the thermodynamic macroscopic variables constitute inexact specifications of the initial conditions, and have their respective "thermodynamic forces". These inexactitudes of specification are the source of the apparent fluctuations that drive the generation of dynamical structure, of the very precise but still less than perfect reproducibility of non-equilibrium experiments, and of the place of entropy in thermodynamics. If one did not know of such inexactitude of specification, one might find the origin of the fluctuations mysterious. What is meant here by "inexactitude of specification" is not that the mean values of the macroscopic variables are inexactly specified, but that the use of macroscopic variables to describe processes that actually occur by the motions and interactions of microscopic objects such as molecules is necessarily lacking in the molecular detail of the processes, and is thus inexact. There are many microscopic states compatible with a single macroscopic state, but only the latter is specified, and that is specified exactly for the purposes of the theory.

其实这种"热力学力"是系统微观初始条件不精确程度的一种表现，用被称为温度的热力学变量<math>T</math>表示。温度只是一个例子，所有的热力学宏观变量都构成了初始条件的不精确规格，都有各自的 "热力学力"。这些不精确的规格是推动动力结构产生明显波动的根源，是非平衡实验非常精确但仍不太完美的重复性的根源，也是熵在热力学中的地位的根源。如果不知道这种不精确的规格，人们可能会觉得波动的起源很神秘。这里所说的 "规格的不精确性"，并不是说宏观变量的均值规定得不精确，而是说用宏观变量来描述分子等微观物体的运动和相互作用实际发生的过程，必然缺乏过程的分子层面细节，因而不精确。有许多微观状态与单一的宏观状态相适应，但只有后者被规定，而这正是为了理论的目的而规定的。

It is reproducibility in repeated observations that identifies dynamical structure in a system. [[Edwin Thompson Jaynes|E.T. Jaynes]]<ref name="Jaynes 1957 I">{{cite journal | last1 = Jaynes | first1 = E.T. | year = 1957 | title = Information theory and statistical mechanics | url = http://bayes.wustl.edu/etj/articles/theory.1.pdf | journal = Physical Review | volume = 106 | issue = 4| pages = 620–630 | doi=10.1103/physrev.106.620| bibcode = 1957PhRv..106..620J }}</ref><ref name="Jaynes 1957 II">{{cite journal | last1 = Jaynes | first1 = E.T. | year = 1957 | title = Information theory and statistical mechanics. II | url = http://bayes.wustl.edu/etj/articles/theory.2.pdf | journal = Physical Review | volume = 108 | issue = 2| pages = 171–190 | doi=10.1103/physrev.108.171| bibcode = 1957PhRv..108..171J }}</ref><ref name="Jaynes 1985">[http://bayes.wustl.edu/etj/articles/macroscopic.prediction.pdf Jaynes, E.T. (1985). Macroscopic prediction, in ''Complex Systems - Operational Approaches in Neurobiology'', edited by H. Haken, Springer-Verlag, Berlin, pp. 254-269] {{ISBN|3-540-15923-1}}.</ref><ref name="Jaynes 1965">{{cite journal | last1 = Jaynes | first1 = E.T. | year = 1965 | title = Gibbs vs Boltzmann Entropies | url = http://bayes.wustl.edu/etj/articles/gibbs.vs.boltzmann.pdf | journal = American Journal of Physics | volume = 33 | issue = 5| pages = 391–398 | doi=10.1119/1.1971557| bibcode = 1965AmJPh..33..391J }}</ref> explains how this reproducibility is why entropy is so important in this topic: entropy is a measure of experimental reproducibility. The entropy tells how many times one would have to repeat the experiment in order to expect to see a departure from the usual reproducible result. When the process goes on in a system with less than a 'practically infinite' number (much much less than Avogadro's or Loschmidt's numbers) of molecules, the thermodynamic reproducibility fades, and fluctuations become easier to see.<ref name="Evans Searles 2002">{{cite journal | last1 = Evans | first1 = D.J. | last2 = Searles | first2 = D.J. | s2cid = 10308868 | year = 2002 | title = The fluctuation theorem | journal = Advances in Physics | volume = 51 | issue = 7| pages = 1529–1585 | doi=10.1080/00018730210155133| bibcode = 2002AdPhy..51.1529E }}</ref><ref name="WSMSE 2002">Wang, G.M., Sevick, E.M., Mittag, E., Searles, D.J., Evans, D.J. (2002) Experimental demonstration of violations of the Second Law of Thermodynamics for small systems and short time scales, ''Physical Review Letters'' 89: 050601-1 - 050601-4.</ref>

It is reproducibility in repeated observations that identifies dynamical structure in a system. E.T. Jaynes explains how this reproducibility is why entropy is so important in this topic: entropy is a measure of experimental reproducibility. The entropy tells how many times one would have to repeat the experiment in order to expect to see a departure from the usual reproducible result. When the process goes on in a system with less than a 'practically infinite' number (much much less than Avogadro's or Loschmidt's numbers) of molecules, the thermodynamic reproducibility fades, and fluctuations become easier to see.

正是重复观测中的可重复性确定了系统中的动态结构。E.T.杰恩斯E.T.Jaynes 解释了这种可重复性是如何解释熵在这个主题中如此重要的原因:熵是实验可重复性的衡量标准。熵告诉人们要重复多少次实验才能期望看到一个偏离通常可重复的结果。当这个过程在一个分子数量少于 "几乎无限 "的系统中进行时（比阿伏加德罗或洛施密特的数量少得多），热力学的可重复性就会减弱，波动就会变得更容易看到。

According to this view of [[Edwin Thompson Jaynes|Jaynes]], it is a common and mystificatory abuse of language, that one often sees reproducibility of dynamical structure called "order".<ref name="Grandy 2008"/><ref name="Dewar 2005">Dewar, R.C. (2005). Maximum entropy production and non-equilibrium statistical mechanics, pp. 41-55 in ''Non-equilibrium Thermodynamics and the Production of Entropy'', edited by A. Kleidon, R.D. Lorenz, Springer, Berlin. {{ISBN|3-540-22495-5}}.</ref> Dewar<ref name="Dewar 2005"/> writes "Jaynes considered reproducibility - rather than disorder - to be the key idea behind the second law of thermodynamics (Jaynes 1963,<ref name="Jaynes 1963">[http://bayes.wustl.edu/etj/articles/brandeis.pdf Jaynes, E.T. (1963). pp. 181-218 in ''Brandeis Summer Institute 1962, Statistical Physics'', edited by K.W. Ford, Benjamin, New York.]</ref> 1965,<ref name="Jaynes 1965"/> 1988,<ref name="Jaynes 1988">[http://bayes.wustl.edu/etj/articles/ccarnot.pdf Jaynes, E.T. (1988). The evolution of Carnot's Principle, pp. 267-282 in ''Maximum-entropy and Bayesian methods in science and engineering'', edited by G.J. Erickson, C.R. Smith, Kluwer, Dordrecht, volume 1] {{ISBN|90-277-2793-7}}.</ref> 1989<ref name="Jaynes 1989">[http://bayes.wustl.edu/etj/articles/cmystery.pdf Jaynes, E.T. (1989). Clearing up mysteries, the original goal, pp. 1-27 in ''Maximum entropy and Bayesian methods'', Kluwer, Dordrecht.]</ref>)." Grandy (2008)<ref name="Grandy 2008"/> in section 4.3 on page 55 clarifies the distinction between the idea that entropy is related to order (which he considers to be an "unfortunate" "mischaracterization" that needs "debunking"), and the aforementioned idea of [[Edwin Thompson Jaynes|Jaynes]] that entropy is a measure of experimental reproducibility of process (which Grandy regards as correct). According to this view, even the admirable book of Glansdorff and Prigogine (1971)<ref name="G&P 1971"/> is guilty of this unfortunate abuse of language.

According to this view of Jaynes, it is a common and mystificatory abuse of language, that one often sees reproducibility of dynamical structure called "order". Dewar "Jaynes considered reproducibility - rather than disorder - to be the key idea behind the second law of thermodynamics (Jaynes 1963,1965,1988,1989)." Grandy (2008) in section 4.3 on page 55 clarifies the distinction between the idea that entropy is related to order (which he considers to be an "unfortunate" "mischaracterization" that needs "debunking"), and the aforementioned idea of Jaynes that entropy is a measure of experimental reproducibility of process (which Grandy regards as correct). According to this view, even the admirable book of Glansdorff and Prigogine (1971)is guilty of this unfortunate abuse of language.

根据Jaynes的这一观点，人们经常看到动态结构的可重复性被称为 "秩序"，这是一种常见的、神秘化的语言滥用。杜瓦 Dewar 写道"Jaynes将可重复性而不是无序性视为是热力学第二定律背后的关键思想（Jaynes1963,1965,1988,1989）"。格兰迪Grandy(2008)在第55页4.3节中阐明了熵与秩序有关的观点之间的区别(他认为熵与秩序有关这是一种 "不幸的""错误描述"，需要 "被揭穿")，以及Jaynes的上述观点，即熵是实验过程可重复性的衡量标准(格兰迪认为这是正确的)。按照这种观点，即使是《Glandsdorff和Prigogine》(1971)这本令人钦佩的书也犯了这种不幸的滥用语言的毛病。

==Local thermodynamic equilibrium==

局部热力学平衡

Various principles have been proposed by diverse authors for over a century. According to Glansdorff and Prigogine (1971, page 15),<ref name="G&P 1971">Glansdorff, P., Prigogine, I. (1971). ''Thermodynamic Theory of Structure, Stability and Fluctuations'', Wiley-Interscience, London. {{ISBN|0-471-30280-5}}</ref> in general, these principles apply only to systems that can be described by thermodynamical variables, in which [[Dissipative system|dissipative processes]] dominate by excluding large deviations from statistical equilibrium. The thermodynamical variables are defined subject to the kinematical requirement of local thermodynamic equilibrium. This means that collisions between molecules are so frequent that chemical and radiative processes do not disrupt the local Maxwell-Boltzmann distribution of molecular velocities.

Various principles have been proposed by diverse authors for over a century. According to Glansdorff and Prigogine (1971, page 15),in general, these principles apply only to systems that can be described by thermodynamical variables, in which dissipative processes dominate by excluding large deviations from statistical equilibrium. The thermodynamical variables are defined subject to the kinematical requirement of local thermodynamic equilibrium. This means that collisions between molecules are so frequent that chemical and radiative processes do not disrupt the local Maxwell-Boltzmann distribution of molecular velocities.

一个多世纪以来，不同的作者提出了各种原则。根据《Glansdorff和Prigogine》(1971年，第15页)，一般来说，这些原则只适用于可以用热力学变量来描述的系统，在这些系统中，耗散过程通过排除统计平衡的巨大偏差而占主导地位。热力学变量的定义要符合局部热力学平衡的运动学要求。这意味着分子之间的碰撞非常频繁，化学和辐射过程不会破坏分子速度的局部麦克斯韦•波兹曼分布。

==Linear and non-linear processes==

线性和非线性过程

[[Dissipative system|Dissipative structures]] can depend on the presence of non-linearity in their dynamical régimes. [[Autocatalytic reactions and order creation|Autocatalytic reactions]] provide examples of non-linear dynamics, and may lead to the natural evolution of [[self-organization|self-organized]] dissipative structures.

Dissipative structures can depend on the presence of non-linearity in their dynamical régimes. Autocatalytic reactions provide examples of non-linear dynamics, and may lead to the natural evolution of self-organized dissipative structures.

耗散结构可能取决于其动态机制中是否存在非线性。自催化反应提供了非线性动态的例子，可能导致自组织耗散结构的自然演变。

==Continuous and discontinuous motions of fluids==

流体的连续和不连续运动

Much of the theory of classical non-equilibrium thermodynamics is concerned with the spatially continuous motion of fluids, but fluids can also move with spatial discontinuities. Helmholtz (1868)<ref name="Helmholtz 1868">Helmholtz, H. (1868). On discontinuous movements of fluids, ''Philosophical Magazine'' series 4, vol. '''36''': 337-346, translated by F. Guthrie from ''Monatsbericht der koeniglich preussischen Akademie der Wissenschaften zu Berlin'' April 1868, page 215 et seq.</ref> wrote about how in a flowing fluid, there can arise a zero fluid pressure, which sees the fluid broken asunder. This arises from the momentum of the fluid flow, showing a different kind of dynamical structure from that of the conduction of heat or electricity. Thus for example: water from a nozzle can form a shower of droplets (Rayleigh 1878,<ref name="Rayleigh 1878">{{cite journal | last1 = Strutt | first1 = J.W. | year = 1878 | title = On the instability of jets | url = https://zenodo.org/record/2095384| journal = Proceedings of the London Mathematical Society | volume = 10 | issue = | pages = 4–13 | doi=10.1112/plms/s1-10.1.4}}</ref> and in section 357 et seq. of Rayleigh (1896/1926)<ref name="Rayleigh 1896/1926">Strutt, J.W. (Baron Rayleigh) (1896/1926). Section 357 et seq. ''The Theory of Sound'', Macmillan, London, reprinted by Dover, New York, 1945.</ref>); waves on the surface of the sea break discontinuously when they reach the shore (Thom 1975<ref name="Thom 1975">Thom, R. (1975). ''Structural Stability and Morphogenesis: An outline of a general theory of models'', translated from the French by D.H. Fowler, W.A. Benjamin, Reading Ma, {{ISBN|0-8053-9279-3}}</ref>). Helmholtz pointed out that the sounds of organ pipes must arise from such discontinuity of flow, occasioned by the passage of air past a sharp-edged obstacle; otherwise the oscillatory character of the sound wave would be damped away to nothing. The definition of the rate of entropy production of such a flow is not covered by the usual theory of classical non-equilibrium thermodynamics. There are many other commonly observed discontinuities of fluid flow that also lie beyond the scope of the classical theory of non-equilibrium thermodynamics, such as: bubbles in boiling liquids and in effervescent drinks; also protected towers of deep tropical convection (Riehl, Malkus 1958<ref name="Riehl Malkus 1958">{{cite journal | last1 = Riehl | first1 = H. | last2 = Malkus | first2 = J.S. | year = 1958 | title = On the heat balance in the equatorial trough zone | url = | journal = Geophysica | volume = 6 | issue = | pages = 503–538 }}</ref>), also called penetrative convection (Lindzen 1977<ref name="Lindzen 1977">Lindzen, R.S. (1977). Some aspects of convection in meteorology, pp. 128-141 in ''Problems of Stellar Convection'', volume 71 of ''Lecture Notes in Physics'', Springer, Berlin, {{ISBN|978-3-540-08532-4}}.</ref>).

Much of the theory of classical non-equilibrium thermodynamics is concerned with the spatially continuous motion of fluids, but fluids can also move with spatial discontinuities. Helmholtz (1868) wrote about how in a flowing fluid, there can arise a zero fluid pressure, which sees the fluid broken asunder. This arises from the momentum of the fluid flow, showing a different kind of dynamical structure from that of the conduction of heat or electricity. Thus for example: water from a nozzle can form a shower of droplets (Rayleigh 1878, and in section 357 et seq. of Rayleigh (1896/1926)); waves on the surface of the sea break discontinuously when they reach the shore (Thom 1975). Helmholtz pointed out that the sounds of organ pipes must arise from such discontinuity of flow, occasioned by the passage of air past a sharp-edged obstacle; otherwise the oscillatory character of the sound wave would be damped away to nothing. The definition of the rate of entropy production of such a flow is not covered by the usual theory of classical non-equilibrium thermodynamics. There are many other commonly observed discontinuities of fluid flow that also lie beyond the scope of the classical theory of non-equilibrium thermodynamics, such as: bubbles in boiling liquids and in effervescent drinks; also protected towers of deep tropical convection (Riehl, Malkus 1958), also called penetrative convection (Lindzen 1977)

经典的非平衡热力学理论大多关注流体的空间连续运动，但流体也可以在空间不连续的情况下运动。赫尔姆霍兹Helmholtz(1868)写道，在流动的流体中，可以出现流体压力为零的情况，这就看到了流体的断裂。这产生于流体流动的动量，显示出与热或电的传导不同的动力结构。因此，例如：从喷头喷出的水可以形成水滴雨（Rayleigh 1878年，以及在Rayleigh（1896/1926）第357节等）；海面上的波浪到达岸边时，会不连续地断裂（Thom 1975）。Helmholtz指出，风琴管的声音一定产生于这种流动的不连续，是由空气经过一个尖锐的障碍物时引起的；否则，声波的振荡特性就会被阻尼掉，化为乌有。这种流动的熵产生率的定义，不是经典非平衡热力学的通常理论所能涵盖的。还有许多经常观察到的流体流动的不连续现象，也不在经典的非平衡热力学理论的范围内，如：沸腾液体中的气泡和泡腾饮料中的气泡；还有受保护的热带深层对流塔（Riehl，Malkus，1958），也叫穿透性对流（Lindzen，1977）。

==Historical development==
发展史
===[[William Thomson, 1st Baron Kelvin|W. Thomson, Baron Kelvin]]===
William Thomson, later Baron Kelvin, (1852 a, 1852 b) wrote

威廉 · 汤姆森，后来的凯尔文男爵(1852年 a，1852年 b)写道

"II. When heat is created by any unreversible process (such as friction), there is a dissipation of mechanical energy, and a full restoration of it to its primitive condition is impossible.

“二.当热是由任何不可逆的过程(如摩擦)产生的时候，就会有机械能的耗散，完全恢复到原始状态是不可能的。

III. When heat is diffused by conduction, there is a dissipation of mechanical energy, and perfect restoration is impossible.

三.当热通过传导扩散时，就会发生机械能的耗散，不可能完全恢复。

IV. When radiant heat or light is absorbed, otherwise than in vegetation, or in a chemical reaction, there is a dissipation of mechanical energy, and perfect restoration is impossible."

四.当辐射热或光被吸收后，除植被外，或在化学反应中，就会发生机械能的耗散，不可能完全恢复。”

In 1854, Thomson wrote about the relation between two previously known non-equilibrium effects. In the Peltier effect, an electric current driven by an external electric field across a bimetallic junction will cause heat to be carried across the junction when the temperature gradient is constrained to zero. In the Seebeck effect, a flow of heat driven by a temperature gradient across such a junction will cause an electromotive force across the junction when the electric current is constrained to zero. Thus thermal and electric effects are said to be coupled. Thomson (1854)<ref name="Kelvin 1854">Thomson, W. (1854). On a mechanical theory of thermo-electric currents, ''Proceedings of the Royal Society of Edinburgh'' pp. 91-98.</ref> proposed a theoretical argument, partly based on the work of Carnot and Clausius, and in those days partly simply speculative, that the coupling constants of these two effects would be found experimentally to be equal. Experiment later confirmed this proposal. It was later one of the ideas that led [[Lars Onsager|Onsager]] to his results as noted below.

In 1854, Thomson wrote about the relation between two previously known non-equilibrium effects. In the Peltier effect, an electric current driven by an external electric field across a bimetallic junction will cause heat to be carried across the junction when the temperature gradient is constrained to zero. In the Seebeck effect, a flow of heat driven by a temperature gradient across such a junction will cause an electromotive force across the junction when the electric current is constrained to zero. Thus thermal and electric effects are said to be coupled. Thomson (1854)proposed a theoretical argument, partly based on the work of Carnot and Clausius, and in those days partly simply speculative, that the coupling constants of these two effects would be found experimentally to be equal. Experiment later confirmed this proposal. It was later one of the ideas that led Onsager to his results as noted below.

1854年，汤姆森Thomson写下了两个以前已知的非平衡效应之间的关系。在佩尔蒂埃效应中，当温度梯度被限制为零时，由外部电场驱动的电流穿过双金属交界处将导致热流穿过该交界处。在塞贝克效应中，当电流被约束为零时，由温度梯度驱动的热流穿过这样的结，将引起结上产生电动势。因此热效应和电效应可以说是耦合的。Thomson(1854)提出了一个理论上的论点，部分是基于卡诺Carnot和克劳修斯Clausius的工作，在当时部分只是推测，这两种效应的耦合常数在实验中会发现是相等的。实验后来证实了这个论点。这也是后来导致Onsager得出他的结果的想法之一，如下所述。

===[[Helmholtz]]===
亥姆霍兹

In 1869, [[Hermann von Helmholtz]] stated his [[Helmholtz minimum dissipation theorem]],<ref>Helmholtz, H. (1869/1871). Zur Theorie der stationären Ströme in reibenden Flüssigkeiten, ''Verhandlungen des naturhistorisch-medizinischen Vereins zu Heidelberg'', Band '''V''': 1-7. Reprinted in Helmholtz, H. (1882), ''Wissenschaftliche Abhandlungen'', volume 1, Johann Ambrosius Barth, Leipzig, pages 223-230 [http://echo.mpiwg-berlin.mpg.de/ECHOdocuViewfull?url=/mpiwg/online/permanent/einstein_exhibition/sources/QWH2FNX8/index.meta&start=231&viewMode=images&pn=237&mode=texttool]</ref> subject to a certain kind of boundary condition, a principle of least viscous dissipation of kinetic energy: "For a steady flow in a viscous liquid, with the speeds of flow on the boundaries of the fluid being given steady, in the limit of small speeds, the currents in the liquid so distribute themselves that the dissipation of kinetic energy by friction is minimum."<ref>from page 2 of Helmholtz 1869/1871, translated by Wikipedia editor.</ref>

In 1869, Hermann von Helmholtz stated his Helmholtz minimum dissipation theorem, subject to a certain kind of boundary condition, a principle of least viscous dissipation of kinetic energy: "For a steady flow in a viscous liquid, with the speeds of flow on the boundaries of the fluid being given steady, in the limit of small speeds, the currents in the liquid so distribute themselves that the dissipation of kinetic energy by friction is minimum."

1869年，赫尔曼•冯•赫尔姆霍兹Hermann von Helmholtz 在一定的边界条件下，陈述了他的Helmholtz最小耗散定理，即动能最小粘性耗散原理："对于粘性液体中的稳定流动，在给定液体边界上的流速稳定的情况下，在速度较小的情况下，液体中的电流如此分布，摩擦力对动能的耗散是最小的。"

In 1878, Helmholtz,<ref name="Helmholtz 1978">{{cite journal | last1 = Helmholtz | first1 = H | year = 1878 | title = Ueber galvanische Ströme, verursacht durch Concentrationsunterschiede; Folgeren aus der mechanischen Wärmetheorie, Wiedermann's | url = https://zenodo.org/record/2343658| journal = Annalen der Physik und Chemie | volume = 3 | issue = 2| pages = 201–216 | doi = 10.1002/andp.18782390204 }}</ref> like Thomson also citing Carnot and Clausius, wrote about electric current in an electrolyte solution with a concentration gradient. This shows a non-equilibrium coupling, between electric effects and concentration-driven diffusion. Like Thomson (Kelvin) as noted above, Helmholtz also found a reciprocal relation, and this was another of the ideas noted by Onsager.

In 1878, Helmholtz, like Thomson also citing Carnot and Clausius, wrote about electric current in an electrolyte solution with a concentration gradient. This shows a non-equilibrium coupling, between electric effects and concentration-driven diffusion. Like Thomson (Kelvin) as noted above, Helmholtz also found a reciprocal relation, and this was another of the ideas noted by Onsager.

1878年，Helmholtz和Thomson一样，也引用了Carnot和Clausius的观点，写出了电解质溶液中的电流与浓度梯度。这表明了一种非平衡耦合，在电效应和浓度驱动的扩散之间。和上面提到的Thomson（开尔文Kelvin）一样，Helmholtz也发现了一种相互关系，这也是Onsager指出的另一个观点。

===[[John William Strutt, 3rd Baron Rayleigh|J. W. Strutt, Baron Rayleigh]]===

Rayleigh (1873)<ref name="Rayleigh 1873">{{cite journal | last1 = Strutt | first1 = J.W. | year = 1873 | title = Some theorems relating to vibrations | url = https://zenodo.org/record/1447754| journal = Proceedings of the London Mathematical Society | volume = 4 | issue = | pages = 357–368 | doi=10.1112/plms/s1-4.1.357}}</ref> (and in Sections 81 and 345 of Rayleigh (1896/1926)<ref name="Rayleigh 1896/1926"/>) introduced the dissipation function for the description of dissipative processes involving viscosity. More general versions of this function have been used by many subsequent investigators of the nature of dissipative processes and dynamical structures. Rayleigh's dissipation function was conceived of from a mechanical viewpoint, and it did not refer in its definition to temperature, and it needed to be 'generalized' to make a dissipation function suitable for use in non-equilibrium thermodynamics.

Rayleigh (1873)(and in Sections 81 and 345 of Rayleigh (1896/1926)) introduced the dissipation function for the description of dissipative processes involving viscosity. More general versions of this function have been used by many subsequent investigators of the nature of dissipative processes and dynamical structures. Rayleigh's dissipation function was conceived of from a mechanical viewpoint, and it did not refer in its definition to temperature, and it needed to be 'generalized' to make a dissipation function suitable for use in non-equilibrium thermodynamics.
Studying jets of water from a nozzle, Rayleigh (1878,1896/1926) noted that when a jet is in a state of conditionally stable dynamical structure, the mode of fluctuation most likely to grow to its full extent and lead to another state of conditionally stable dynamical structure is the one with the fastest growth rate. In other words, a jet can settle into a conditionally stable state, but it is likely to suffer fluctuation so as to pass to another, less unstable, conditionally stable state. He used like reasoning in a study of Bénard convection.These physically lucid considerations of Rayleigh seem to contain the heart of the distinction between the principles of minimum and maximum rates of dissipation of energy and entropy production, which have been developed in the course of physical investigations by later authors.

Rayleigh(1873)(以及Rayleigh(1896/1926)的第81和345节)引入了耗散函数，用于描述涉及粘度的耗散过程。这个函数的更多通用版本已经被许多后来的研究者用来研究耗散过程和动力学结构的性质。Rayleigh的耗散函数是从力学的角度设想的，它的定义中并没有提到温度，它需要被 "泛化"，使耗散函数适合用于非平衡热力学。
Rayleigh(1878,1896/1926)在研究喷头的射流时指出，当射流处于条件稳定的动力结构状态时，最有可能增长到其全部程度并导致另一种条件稳定的动力结构状态的波动模式是增长速度最快的模式。换句话说，一个喷流可以稳定在一个条件稳定的状态，但它很可能遭受波动，从而传递到另一个不那么不稳定的条件稳定状态。他在对贝纳德Bénard对流的研究中使用了类似的推理。Rayleigh的这些物理上的明晰考虑似乎包含了能量耗散和熵产生的最小速率和最大速率原则的区别的核心，这些原则在后来的物理研究过程中得到了发展。

===[[Diederik Korteweg|Korteweg]]===
科特韦格

Korteweg (1883)<ref name="Korteweg 1883">{{cite journal | last1 = Korteweg | first1 = D.J. | year = 1883 | title = On a general theorem of the stability of the motion of a viscous fluid | url = https://zenodo.org/record/1431165| journal = The London, Edinburgh and Dublin Philosophical Journal of Science | volume = 16 | issue = 98| pages = 112–118 | doi=10.1080/14786448308627405}}</ref> gave a proof "that in any simply connected region, when the velocities along the boundaries are given, there exists, as far as the squares and products of the velocities may be neglected, only one solution of the equations for the steady motion of an incompressible viscous fluid, and that this solution is always stable." He attributed the first part of this theorem to Helmholtz, who had shown that it is a simple consequence of a theorem that "if the motion be steady, the currents in a viscous [incompressible] fluid are so distributed that the loss of [kinetic] energy due to viscosity is a minimum, on the supposition that the velocities along boundaries of the fluid are given." Because of the restriction to cases in which the squares and products of the velocities can be neglected, these motions are below the threshold for turbulence.

Korteweg (1883) gave a proof "that in any simply connected region, when the velocities along the boundaries are given, there exists, as far as the squares and products of the velocities may be neglected, only one solution of the equations for the steady motion of an incompressible viscous fluid, and that this solution is always stable." He attributed the first part of this theorem to Helmholtz, who had shown that it is a simple consequence of a theorem that "if the motion be steady, the currents in a viscous [incompressible] fluid are so distributed that the loss of [kinetic] energy due to viscosity is a minimum, on the supposition that the velocities along boundaries of the fluid are given." Because of the restriction to cases in which the squares and products of the velocities can be neglected, these motions are below the threshold for turbulence.

Korteweg (1883)证明了“在任何简单连接的区域，当沿边界的速度给定时，只要速度的平方和乘积可以忽略，就存在一个不可压缩粘性流体稳定运动方程的唯一解，而且这个解总是稳定的"。他把这个定理的第一部分归功于Helmholtz，他曾证明，这是一个定理的简单结果，即 "如果运动是稳定的，那么在给定沿流体边界的速度的前提下，粘性[不可压缩]流体中的电流是如此分布，以至于粘性引起的[动能]损失是最小的"。"由于限制在速度的平方和乘积可以忽略的情况下，这些运动低于湍流的阈值。
===[[Lars Onsager|Onsager]]===
昂萨格

Great theoretical progress was made by Onsager in 1931<ref name="Onsager 1931 I"/><ref name="Onsager 1931 II">{{cite journal | last1 = Onsager | first1 = L | year = 1931 | title = Reciprocal relations in irreversible processes. II | url = | journal = Physical Review | volume = 38 | issue = 12| pages = 2265–2279 | doi=10.1103/physrev.38.2265| bibcode = 1931PhRv...38.2265O| doi-access = free }}</ref> and in 1953.<ref name="Onsager Machlup 1953">{{cite journal | last1 = Onsager | first1 = L. | last2 = Machlup | first2 = S. | year = 1953 | title = Fluctuations and Irreversible Processes | url = | journal = Physical Review | volume = 91 | issue = 6| pages = 1505–1512 | doi=10.1103/physrev.91.1505| bibcode = 1953PhRv...91.1505O }}</ref><ref name="Machlup Onsager 1953">{{cite journal | last1 = Machlup | first1 = S. | last2 = Onsager | first2 = L. | year = 1953 | title = Fluctuations and Irreversible Processes. II. Systems with kinetic energy | url = | journal = Physical Review | volume = 91 | issue = 6| pages = 1512–1515 | doi=10.1103/physrev.91.1512| bibcode = 1953PhRv...91.1512M }}</ref>

Great theoretical progress was made by Onsager in 1931 and in 1953.

Onsager 1931年和1953年在理论上取得了重大进展。

===[[Ilya Prigogine|Prigogine]]===
普利戈金

Further progress was made by Prigogine in 1945<ref name="Prigogine 1945">{{cite journal | last1 = Prigogine | first1 = I | year = 1945 | title = Modération et transformations irréversibles des systèmes ouverts | url = | journal = Bulletin de la Classe des Sciences., Académie Royale de Belgique | volume = 31 | issue = | pages = 600–606 }}</ref> and later.<ref name="G&P 1971"/><ref name="Prigogine 1947">Prigogine, I. (1947). ''Étude thermodynamique des Phenomènes Irréversibles'', Desoer, Liège.</ref> Prigogine (1947)<ref name="Prigogine 1945"/> cites Onsager (1931).<ref name="Onsager 1931 I"/><ref name="Onsager 1931 II"/>

Further progress was made by Prigogine in 1945 and later. Prigogine (1947) extended the theory of Onsager.

Prigogine在1945年及其后取得了进一步的进展。Prigogine(1947)扩展了Onsager的理论。

===[[Hendrik Casimir|Casimir]]===
卡西米尔
Casimir (1945)<ref name="Casimir 1945">{{cite journal | last1 = Casimir | first1 = H.B.G. | s2cid = 53386496 | year = 1945 | title = On Onsager's principle of microscopic reversibility | journal = Reviews of Modern Physics | volume = 17 | issue = 2–3| pages = 343–350 | doi=10.1103/revmodphys.17.343| bibcode = 1945RvMP...17..343C}}</ref> extended the theory of Onsager.

Casimir (1945)extended the theory of Onsager.
Casimir（1945）扩展了Onsager理论。

===[[John Ziman|Ziman]]===
齐曼

Ziman (1956)<ref name="Ziman 1956">{{cite journal | last1 = Ziman | first1 = J.M. | year = 1956 | title = The general variational principle of transport theory | url = | journal = Canadian Journal of Physics | volume = 34 | issue = 12A| pages = 1256–1273 | doi=10.1139/p56-139| bibcode = 1956CaJPh..34.1256Z}}</ref> gave very readable account. He proposed the following as a general principle of the thermodynamics of irreversible processes: "''Consider all distributions of currents such that the intrinsic entropy production equals the extrinsic entropy production for the given set of forces. Then, of all current distributions satisfying this condition, the steady state distribution makes the entropy production a maximum.''" He commented that this was a known general principle, discovered by Onsager, but was "not quoted in any of the books on the subject". He notes the difference between this principle and "Prigogine's theorem, which states, crudely speaking, that if not all the forces acting on a system are fixed the free forces will take such values as to make the entropy production a minimum." Prigogine was present when this paper was read and he is reported by the journal editor to have given "notice that he doubted the validity of part of Ziman's thermodynamic interpretation".

Ziman (1956) gave very readable account. He proposed the following as a general principle of the thermodynamics of irreversible processes: "Consider all distributions of currents such that the intrinsic entropy production equals the extrinsic entropy production for the given set of forces. Then, of all current distributions satisfying this condition, the steady state distribution makes the entropy production a maximum." He commented that this was a known general principle, discovered by Onsager, but was "not quoted in any of the books on the subject". He notes the difference between this principle and "Prigogine's theorem, which states, crudely speaking, that if not all the forces acting on a system are fixed the free forces will take such values as to make the entropy production a minimum." Prigogine was present when this paper was read and he is reported by the journal editor to have given "notice that he doubted the validity of part of Ziman's thermodynamic interpretation".

Ziman(1956)给出了非常易读的描述。他提出了以下内容作为不可逆过程热力学的一般原则。"考虑所有的电流分布使得在给定的力的作用下内在熵的产生等于外在熵的产生"。那么，在所有满足这一条件的电流分布中，稳态分布使熵产量达到最大值。" 他评论说，这是一个众所周知的一般原理，是由Onsager发现的，但 "在任何有关的书籍中都没有被引用"。他注意到这一原理与 "Prigogine定理 "的区别，Prigogine定理粗略地说，如果不是所有作用在一个系统上的力都是固定的，那么自由力就会取这样的值，使熵的产生成为最小值"。"宣读这篇论文时，Prigogine在场，据期刊编辑报道说，他曾发通知说，他怀疑Ziman的热力学解释的有效性"。

===Ziegler===
齐格勒
[[Hans Ziegler (physicist)|Hans Ziegler]] extended the Melan-Prager non-equilibrium theory of materials to the non-isothermal case.<ref>T. Inoue (2002). Metallo-Thermo-Mechanics–Application to Quenching. ''In'' G. Totten, M. Howes, and T. Inoue (eds.), Handbook of Residual Stress. pp. 296-311, ASM International, Ohio.</ref>

Hans Ziegler extended the Melan-Prager non-equilibrium theory of materials to the non-isothermal case.

Hans Ziegler 将材料的 Melan-Prager 非平衡理论扩展到了非等温情况。

===Gyarmati===
乔尔玛蒂
Gyarmati (1967/1970)<ref name="Gyarmati 1970">Gyarmati, I. (1970). ''Non-equilibrium Thermodynamics: Field Theory and Variational Principles'', Springer, Berlin; translated, by E. Gyarmati and W.F. Heinz, from the original 1967 Hungarian ''Nemegyensulyi Termodinamika'', Muszaki Konyvkiado, Budapest.</ref> gives a systematic presentation, and extends Onsager's principle of least dissipation of energy, to give a more symmetric form known as Gyarmati's principle. Gyarmati (1967/1970)<ref name="Gyarmati 1970"/> cites 11 papers or books authored or co-authored by Prigogine.

Gyarmati (1967/1970)<ref name="Gyarmati 1970"/> also gives in Section III 5 a very helpful precis of the subtleties of Casimir (1945)).<ref name="Casimir 1945"/> He explains that the Onsager reciprocal relations concern variables which are even functions of the velocities of the molecules, and notes that Casimir went on to derive anti-symmetric relations concerning variables which are odd functions of the velocities of the molecules.

Gyarmati (1967/1970) gives a systematic presentation, and extends Onsager's principle of least dissipation of energy, to give a more symmetric form known as Gyarmati's principle. Gyarmati (1967/1970) cites 11 papers or books authored or co-authored by Prigogine. Gyarmati (1967/1970)also gives in Section III 5 a very helpful precis of the subtleties of Casimir (1945)).He explains that the Onsager reciprocal relations concern variables which are even functions of the velocities of the molecules, and notes that Casimir went on to derive anti-symmetric relations concerning variables which are odd functions of the velocities of the molecules.
Gyarmati(1967/1970)给出了一个系统的表述，并扩展了Onsager的能量最小耗散原理，给出了一个更对称的形式，称为Gyarmati原理。Gyarmati(1967/1970)引用了11篇Prigogine撰写或合著的论文或书籍。Gyarmati (1967/1970)还在第三节5中对Casimir (1945)的微妙之处给出了一个非常有用的预言.他解释说，Onsager往复关系涉及的变量是分子速度的偶数函数，并指出Casimir继续推导出反对称关系，涉及的变量是分子速度的奇数函数。

===Paltridge===
帕特里奇

The physics of the earth's atmosphere includes dramatic events like lightning and the effects of volcanic eruptions, with discontinuities of motion such as noted by Helmholtz (1868).<ref name="Helmholtz 1868"/> Turbulence is prominent in atmospheric convection. Other discontinuities include the formation of raindrops, hailstones, and snowflakes. The usual theory of classical non-equilibrium thermodynamics will need some extension to cover atmospheric physics. According to Tuck (2008),<ref name="Tuck, Adrian F. 2008 page 33">Tuck, Adrian F. (2008) ''Atmospheric Turbulence: a molecular dynamics perspective'', Oxford University Press. {{ISBN|978-0-19-923653-4}}. See page 33.</ref> "On the macroscopic level, the way has been pioneered by a meteorologist (Paltridge 1975,<ref name="Paltridge 1975">Paltridge, G.W. (1975). Global dynamics and climate - a system of minimum entropy exchange, ''Quarterly Journal of the Royal Meteorological Society 101:475-484.

[http://onlinelibrary.wiley.com/doi/10.1002/qj.49710142906/full]

</ref> 2001<ref>{{cite journal | last1 = Paltridge | first1 = G.W. | year = 2001 | title = A physical basis for a maximum of thermodynamic dissipation of the climate system | url = http://www3.interscience.wiley.com/journal/114028007/abstract | archive-url = https://archive.today/20121018022835/http://www3.interscience.wiley.com/journal/114028007/abstract | url-status = dead | archive-date = 2012-10-18 | journal = Quarterly Journal of the Royal Meteorological Society | volume = 127 | issue = 572| pages = 305–313 | doi=10.1256/smsqj.57202}}</ref>). Initially Paltridge (1975)<ref name="Paltridge 1975"/> used the terminology "minimum entropy exchange", but after that, for example in Paltridge (1978),<ref name="Paltridge 1978">{{cite journal | last1 = Paltridge | first1 = G.W. | year = 1978 | title = The steady-state format of global climate | url = | journal = Quarterly Journal of the Royal Meteorological Society | volume = 104 | issue = 442| pages = 927–945 | doi=10.1256/smsqj.44205}}</ref> and in Paltridge (1979)<ref>{{cite journal | last1 = Paltridge | first1 = G.W. | year = 1979 | title = Climate and thermodynamic systems of maximum dissipation | journal = Nature | volume = 279 | issue = 5714| pages = 630–631 | bibcode=1979Natur.279..630P | doi=10.1038/279630a0| s2cid = 4262395 }}</ref>), he used the now current terminology "maximum entropy production" to describe the same thing. This point is clarified in the review by Ozawa, Ohmura, Lorenz, Pujol (2003).<ref name="OOLP 2003">{{cite journal | last1 = Ozawa | first1 = H. | last2 = Ohmura | first2 = A. | last3 = Lorenz | first3 = R.D. | last4 = Pujol | first4 = T. | year = 2003 | title = The Second Law of Thermodynamics and the Global Climate System: A Review of the Maximum Entropy Production Principle | url = http://homepage.mac.com/bradmarston/Papers/Ozawa%20etal%20(2003).pdf | journal = Reviews of Geophysics | volume = 41 | issue = 4| pages = 1–24 | doi=10.1029/2002rg000113 | bibcode=2003RvGeo..41.1018O| hdl = 10256/8489 }}</ref> Paltridge (1978)<ref name="Paltridge 1978"/> cited Busse's (1967)<ref>{{cite journal | last1 = Busse | first1 = F.H. | year = 1967 | title = The stability of finite amplitude cellular convection and its relation to an extremum principle | url = | journal = Journal of Fluid Mechanics | volume = 30 | issue = 4| pages = 625–649 | doi=10.1017/s0022112067001661| bibcode = 1967JFM....30..625B}}</ref> fluid mechanical work concerning an extremum principle. Nicolis and Nicolis (1980) <ref name="Nicolis 1980">{{cite journal | last1 = Nicolis | first1 = G. | last2 = Nicolis | first2 = C. | year = 1980 | title = On the entropy balance of the earth-atmosphere system | url = | journal = Quarterly Journal of the Royal Meteorological Society | volume = 106 | issue = 450| pages = 691–706| doi = 10.1002/qj.49710645003 | bibcode = 1980QJRMS.106..691N }}</ref> discuss Paltridge's work, and they comment that the behaviour of the entropy production is far from simple and universal. This seems natural in the context of the requirement of some classical theory of non-equilibrium thermodynamics that the threshold of turbulence not be crossed. Paltridge himself nowadays tends to prefer to think in terms of the dissipation function rather than in terms of rate of entropy production.

The physics of the earth's atmosphere includes dramatic events like lightning and the effects of volcanic eruptions, with discontinuities of motion such as noted by Helmholtz (1868).Turbulence is prominent in atmospheric convection. Other discontinuities include the formation of raindrops, hailstones, and snowflakes. The usual theory of classical non-equilibrium thermodynamics will need some extension to cover atmospheric physics. According to Tuck (2008),"On the macroscopic level, the way has been pioneered by a meteorologist (Paltridge 1975,2001). Initially Paltridge (1975)used the terminology "minimum entropy exchange", but after that, for example in Paltridge (1978),and in Paltridge (1979)), he used the now current terminology "maximum entropy production" to describe the same thing. This point is clarified in the review by Ozawa, Ohmura, Lorenz, Pujol (2003).Paltridge (1978)cited Busse's (1967)fluid mechanical work concerning an extremum principle. Nicolis and Nicolis (1980) discuss Paltridge's work, and they comment that the behaviour of the entropy production is far from simple and universal. This seems natural in the context of the requirement of some classical theory of non-equilibrium thermodynamics that the threshold of turbulence not be crossed. Paltridge himself nowadays tends to prefer to think in terms of the dissipation function rather than in terms of rate of entropy production.

地球大气的物理学包括像闪电这样的戏剧性事件和火山喷发的影响，具有运动的不连续性，如Helmholtz（1868）所指出的那样湍流在大气对流中很突出。其他不连续性包括雨滴、冰雹和雪花的形成。通常的经典非平衡热力学理论将需要一些扩展来涵盖大气物理学。根据Tuck(2008)的说法，"在宏观层面上，这种方式是由一位气象学家开创的(Paltridge 1975，2001)。最初Paltridge(1975)[50]使用了 "最小熵交换 "的术语，但之后，例如在Paltridge(1978)、和Paltridge(1979))中，他使用了现在的术语 "最大熵生产 "来描述同样的事情。这一点在Ozawa、Ohmura、Lorenz、Pujol(2003)的综述中得到了澄清.Paltridge(1978)引用了Busse(1967)关于极限原理的流体力学工作。Nicolis和Nicolis(1980)讨论了Paltridge的工作，他们评论说，熵的产生行为远非简单和普遍。这在一些经典的非平衡热力学理论要求不越过湍流阈值的情况下，似乎是很自然的。Paltridge本人现在往往喜欢从耗散函数的角度而不是从熵的产生速率的角度来考虑。

==Speculated thermodynamic extremum principles for energy dissipation and entropy production==

用于能量耗散和熵产生的推测热力学极值原理

Jou, Casas-Vazquez, Lebon (1993)<ref name="JCVL 1993">Jou, D., Casas-Vázquez, J., Lebon, G. (1993). ''Extended Irreversible Thermodynamics'', Springer, Berlin, {{ISBN|3-540-55874-8}}, {{ISBN|0-387-55874-8}}.</ref> note that classical non-equilibrium thermodynamics "has seen an extraordinary expansion since the second world war", and they refer to the Nobel prizes for work in the field awarded to [[Lars Onsager]] and [[Ilya Prigogine]]. Martyushev and Seleznev (2006)<ref name="M&S 2006"/> note the importance of entropy in the evolution of natural dynamical structures: "Great contribution has been done in this respect by two scientists, namely [[Rudolf Clausius|Clausius]], ... , and [[Ilya Prigogine|Prigogine]]." Prigogine in his 1977 Nobel Lecture<ref>[http://nobelprize.org/nobel_prizes/chemistry/laureates/1977/prigogine-lecture.pdf Prigogine, I. (1977). Time, Structure and Fluctuations, Nobel Lecture.]</ref> said: "... non-equilibrium may be a source of order. Irreversible processes may lead to a new type of dynamic states of matter which I have called “dissipative structures”." Glansdorff and Prigogine (1971)<ref name="G&P 1971"/> wrote on page xx: "Such 'symmetry breaking instabilities' are of special interest as they lead to a spontaneous 'self-organization' of the system both from the point of view of its ''space order'' and its ''function''."

Analyzing the [[Rayleigh–Bénard convection|Rayleigh–Bénard convection cell phenomenon]], Chandrasekhar (1961)<ref>Chandrasekhar, S. (1961). ''Hydrodynamic and Hydromagnetic Stability'', Clarendon Press, Oxford.</ref> wrote "Instability occurs at the minimum temperature gradient at which a balance can be maintained between the kinetic energy dissipated by viscosity and the internal energy released by the buoyancy force." With a temperature gradient greater than the minimum, viscosity can dissipate kinetic energy as fast as it is released by convection due to buoyancy, and a steady state with convection is stable. The steady state with convection is often a pattern of macroscopically visible hexagonal cells with convection up or down in the middle or at the 'walls' of each cell, depending on the temperature dependence of the quantities; in the atmosphere under various conditions it seems that either is possible. (Some details are discussed by Lebon, Jou, and Casas-Vásquez (2008)<ref name="Lebon Jou Casas-Vázquez 2008"/> on pages 143–158.) With a temperature gradient less than the minimum, viscosity and heat conduction are so effective that convection cannot keep going.

Glansdorff and Prigogine (1971)<ref name="G&P 1971"/> on page xv wrote "Dissipative structures have a quite different [from equilibrium structures] status: they are formed and maintained through the effect of exchange of energy and matter in non-equilibrium conditions." They were referring to the dissipation function of Rayleigh (1873)<ref name="Rayleigh 1873"/> that was used also by Onsager (1931, I,<ref name="Onsager 1931 I"/> 1931, II<ref name="Onsager 1931 II"/>). On pages 78–80 of their book<ref name="G&P 1971"/> Glansdorff and Prigogine (1971) consider the stability of laminar flow that was pioneered by Helmholtz; they concluded that at a stable steady state of sufficiently slow laminar flow, the dissipation function was minimum.

Jou, Casas-Vazquez, Lebon (1993)note that classical non-equilibrium thermodynamics "has seen an extraordinary expansion since the second world war", and they refer to the Nobel prizes for work in the field awarded to Lars Onsager and Ilya Prigogine. Martyushev and Seleznev (2006)note the importance of entropy in the evolution of natural dynamical structures: "Great contribution has been done in this respect by two scientists, namely Clausius, ... , and Prigogine." Prigogine in his 1977 Nobel Lecture said: "... non-equilibrium may be a source of order. Irreversible processes may lead to a new type of dynamic states of matter which I have called “dissipative structures”." Glansdorff and Prigogine (1971) wrote on page xx: "Such 'symmetry breaking instabilities' are of special interest as they lead to a spontaneous 'self-organization' of the system both from the point of view of its space order and its function."
Analyzing the Rayleigh–Bénard convection cell phenomenon, Chandrasekhar (1961) wrote "Instability occurs at the minimum temperature gradient at which a balance can be maintained between the kinetic energy dissipated by viscosity and the internal energy released by the buoyancy force." With a temperature gradient greater than the minimum, viscosity can dissipate kinetic energy as fast as it is released by convection due to buoyancy, and a steady state with convection is stable. The steady state with convection is often a pattern of macroscopically visible hexagonal cells with convection up or down in the middle or at the 'walls' of each cell, depending on the temperature dependence of the quantities; in the atmosphere under various conditions it seems that either is possible. (Some details are discussed by Lebon, Jou, and Casas-Vásquez (2008) on pages 143–158.) With a temperature gradient less than the minimum, viscosity and heat conduction are so effective that convection cannot keep going.
Glansdorff and Prigogine (1971) on page xv wrote "Dissipative rstructures have a quite different [from equilibrium structures] status: they are formed and maintained through the effect of exchange of energy and matter in non-equilibrium conditions." They were referring to the dissipation function of Rayleigh (1873) that was used also by Onsager (1931, I,1931, II). On pages 78–80 of their book Glansdorff and Prigogine (1971) consider the stability of laminar flow that was pioneered by Helmholtz; they concluded that at a stable steady state of sufficiently slow laminar flow, the dissipation function was minimum.
These advances have led to proposals for various extremal principles for the "self-organized" régimes that are possible for systems governed by classical linear and non-linear non-equilibrium thermodynamical laws, with stable stationary régimes being particularly investigated. Convection introduces effects of momentum which appear as non-linearity in the dynamical equations. In the more restricted case of no convective motion, Prigogine wrote of "dissipative structures". Šilhavý (1997) offers the opinion that "... the extremum principles of [equilibrium] thermodynamics ... do not have any counterpart for [non-equilibrium] steady states (despite many claims in the literature)."

Jou、Casas-Vazquez、Lebon(1993)指出，经典非平衡热力学 "自第二次世界大战以来得到了非凡的发展"，他们指的是诺贝尔奖获得者Lars Onsager和Ilya Prigogine。 Martyushev和Seleznev(2006)指出了熵在自然动力结构演化中的重要性。"在这方面，两位科学家，例如Clausius和Prigogine做出了巨大贡献。” Prigogine在1977年的诺贝尔演讲中说："... 非平衡可能是秩序的源泉。不可逆的过程可能导致一种新的物质动态状态，我称之为 "耗散结构" 。Glansdorff和Prigogine(1971)在第xx页上写道："这种'对称性破坏的不稳定性'特别令人关注，因为它们从系统的空间秩序和功能的角度来看，都会导致系统自发的'自组织'。"
Chandrasekhar(1961)在分析Rayleigh-Bénard对流池现象时写道："不稳定性发生在最小温度梯度处，在这个温度梯度上，粘度所耗散的动能和浮力所释放的内能之间可以保持平衡。" 在温度梯度大于最小值的情况下，由于浮力的作用，粘度散失的动能与对流释放的动能一样快，有对流的稳态是稳定的。有对流的稳态往往是宏观可见的六边形单元的模式，每个单元的中间或 "壁 "处都有上下对流，这取决于量的温度依赖性；在大气中的各种条件下，似乎两种情况都有可能。一些细节由Lebon、Jou和Casasas-Vásquez（2008）在第143-158页上讨论。在温度梯度小于最小值的情况下，粘度和热传导非常有效，以至于对流无法继续进行。
Glansdorff和Prigogine(1971)在第xv页上写道："耗散结构具有完全不同的[与平衡结构]地位：它们是通过非平衡条件下能量和物质交换的作用形成和维持的"。他们指的是雷利(1873)的耗散函数，Onsager(1931,I,1931,II)也使用了这个函数。在他们的书的78-80页上，Glansdorff和Prigogine(1971)考虑了由Helmholtz开创的层流的稳定性；他们的结论是，在足够慢的层流的稳定稳态下，耗散函数是最小的。
这些进展导致了对经典线性和非线性非平衡热力学定律所控制的系统可能出现的 "自组织 "规则的各种极限原理的提出，其中稳定的静止规则被特别研究。对流引入了动量的影响，在动力学方程中表现为非线性。在没有对流运动的情况下，Prigogine写道 "耗散结构"。Šilhavý(1997年)提出了这样的观点："平衡热力学的极端原则对于非平衡稳定状态没有任何对应的原则(尽管文献中有许多说法)"。

==Prigogine's proposed theorem of minimum entropy production for very slow purely diffusive transfer==

Prigogine提出的用于极慢的纯扩散转移的最小熵产生定理。

In 1945 Prigogine (see also Prigogine (1947)) proposed a “Theorem of Minimum Entropy Production” which applies only to the purely diffusive linear regime, with negligible inertial terms, near a stationary thermodynamically non-equilibrium state. Prigogine's proposal is that the rate of entropy production is locally minimum at every point. The proof offered by Prigogine is open to serious criticism. A critical and unsupportive discussion of Prigogine's proposal is offered by Grandy (2008). It has been shown by Barbera that the total whole body entropy production cannot be minimum, but this paper did not consider the pointwise minimum proposal of Prigogine. A proposal closely related to Prigogine's is that the pointwise rate of entropy production should have its maximum value minimized at the steady state. This is compatible, but not identical, with the Prigogine proposal. Moreover, N. W. Tschoegl proposes a proof, perhaps more physically motivated than Prigogine's, that would if valid support the conclusion of Helmholtz and of Prigogine, that under these restricted conditions, the entropy production is at a pointwise minimum.

1945年Prigogine(另见Prigogine(1947))提出了 "最小熵产生定理"，该定理只适用于静止的热力学非平衡状态附近的纯扩散线性体系，惯性项可忽略不计。Prigogine提出的是熵的产生速率在每一点上都是局部最小的。Prigogine提出的证明受到了严重的批评。Grandy(2008)对Prigogine的提议进行了批判性的和不支持的讨论。Barbera已经证明了全身熵产不能最小，但本文没有考虑Prigogine的点最小建议。与Prigogine的提议密切相关的是，熵产生的点率在稳态时应该有其最大值最小化。这与Prigogine的建议是一致的，但不完全相同。此外，N.W.Tschoegl提出了一个证明，也许比Prigogine的证明更有物理动机，如果有效的话，它将支持Helmholtz和Prigogine的结论，即在这些限制条件下，熵的产生是在一个点上最小的。

== Faster transfer with convective circulation: second entropy ==

更快的对流环流转移：第二熵

In contrast to the case of sufficiently slow transfer with linearity between flux and generalized force with negligible inertial terms, there can be heat transfer that is not very slow. Then there is consequent non-linearity, and heat flow can develop into phases of convective circulation. In these cases, the time rate of entropy production has been shown to be a non-monotonic function of time during the approach to steady state heat convection. This makes these cases different from the near-thermodynamic-equilibrium regime of very-slow-transfer with linearity. Accordingly, the local time rate of entropy production, defined according to the local thermodynamic equilibrium hypothesis, is not an adequate variable for prediction of the time course of far-from-thermodynamic equilibrium processes. The principle of minimum entropy production is not applicable to these cases.

与通量和广义力之间具有线性的足够慢的传递，惯性项可忽略不计的情况相反，可以有不是很慢的热传递。那么随之而来的是非线性，热流可以发展成对流循环的阶段。在这些情况下，在接近稳态热对流的过程中，熵产生的时间速率已被证明是一个非单调的时间函数。这使得这些情况不同于近热动力-平衡体制的极慢-转移的线性。因此，根据局部热力学平衡假说所定义的熵产生的局部时间速率，并不是预测远-热力学平衡过程的时间过程的充分变量。最小熵产生原则不适用于这些情况。

To cover these cases, there is needed at least one further state variable, a non-equilibrium quantity, the so-called second entropy. This appears to be a step towards generalization beyond the classical second law of thermodynamics, to cover non-equilibrium states or processes. The classical law refers only to states of thermodynamic equilibrium, and local thermodynamic equilibrium theory is an approximation that relies upon it. Still it is invoked to deal with phenomena near but not at thermodynamic equilibrium, and has some uses then. But the classical law is inadequate for description of the time course of processes far from thermodynamic equilibrium. For such processes, a more powerful theory is needed, and the second entropy is part of such a theory.

为了涵盖这些情况，至少还需要一个状态变量，一个非平衡量，即所谓的第二熵。这似乎是向着超越经典热力学第二定律的泛化方向迈出的一步，以涵盖非平衡状态或过程。经典定律只指热力学平衡状态，局部热力学平衡理论是依靠它的近似。但在处理接近但不处于热力学平衡状态的现象时，还是会引用它，那时有一定的用途。但对于远离热力学平衡的过程的时间过程的描述，经典定律是不够的。对于这样的过程，需要一个更强大的理论，而第二熵就是这种理论的一部分。

== Speculated principles of maximum entropy production and minimum energy dissipatio==

最大熵的产生和最小能量耗散的推测原理。

Onsager (1931, I)wrote: "Thus the vector field J of the heat flow is described by the condition that the rate of increase of entropy, less the dissipation function, be a maximum." Careful note needs to be taken of the opposite signs of the rate of entropy production and of the dissipation function, appearing in the left-hand side of Onsager's equation (5.13) on Onsager's page 423.

Onsager(1931，I)写道："因此，热流的矢量场J是由熵的增加率减去耗散函数的条件来描述的，是一个最大值。" 需要仔细注意的是，在Onsager第423页的Onsager方程(5.13)左侧出现的熵产生率和耗散函数的相反符号。

Although largely unnoticed at the time, Ziegler proposed an idea early with his work in the mechanics of plastics in 1961,and later in his book on thermomechanics revised in 1983,and in various papers (e.g., Ziegler (1987),). Ziegler never stated his principle as a universal law but he may have intuited this. He demonstrated his principle using vector space geometry based on an “orthogonality condition” which only worked in systems where the velocities were defined as a single vector or tensor, and thus, as he wrote at p. 347, was “impossible to test by means of macroscopic mechanical models”, and was, as he pointed out, invalid in “compound systems where several elementary processes take place simultaneously”.
In relation to the earth's atmospheric energy transport process, according to Tuck (2008), "On the macroscopic level, the way has been pioneered by a meteorologist (Paltridge 1975,2001)." Initially Paltridge (1975)used the terminology "minimum entropy exchange", but after that, for example in Paltridge (1978),and in Paltridge (1979),he used the now current terminology "maximum entropy production" to describe the same thing. The logic of Paltridge's earlier work is open to serious criticism.Nicolis and Nicolis (1980) discuss Paltridge's work, and they comment that the behaviour of the entropy production is far from simple and universal. Later work by Paltridge focuses more on the idea of a dissipation function than on the idea of rate of production of entropy.
Sawada (1981),also in relation to the Earth's atmospheric energy transport process, postulating a principle of largest amount of entropy increment per unit time, cites work in fluid mechanics by Malkus and Veronis (1958) as having "proven a principle of maximum heat current, which in turn is a maximum entropy production for a given boundary condition", but this inference is not logically valid. Again investigating planetary atmospheric dynamics, Shutts (1981) used an approach to the definition of entropy production, different from Paltridge's, to investigate a more abstract way to check the principle of maximum entropy production, and reported a good fit.

虽然当时基本上没有被注意到，但Ziegler很早就在1961年的塑料力学工作中提出了一个想法，后来又在1983年修订的热力学书中和各种论文中提出了这个想法（例如，Ziegler（1987））。Ziegler从来没有说过他的原则作为一个普遍的法律，但他可能已经直观地了解到这一点。他使用基于 "正交条件 "的矢量空间几何学来证明他的原理，该条件只在速度被定义为单一矢量或张量的系统中起作用，因此，正如他在第347页中所写的那样，"不可能通过宏观机械模型来检验"，而且正如他所指出的那样，在 "几个基本过程同时发生的复合系统 "中是无效的。
关于地球大气能量传输过程，根据Tuck(2008)的说法，"在宏观层面上，这种方式是由一位气象学家开创的(Paltridge 1975年，2001年)"。最初Paltridge(1975)使用了 "最小熵交换 "的术语，但此后，例如在Paltridge(1978)中，以及在Paltridge(1979)中，他使用了现在的术语 "最大熵生产 "来描述同样的事情。Paltridge早期工作的逻辑受到了严重的批评.Nicolis和Nicolis(1980)讨论了Paltridge的工作,他们评论说,熵生产的行为远非简单和普遍。Paltridge后来的工作更多的关注于耗散函数的概念，而不是熵的产生速率的概念。
Sawada(1981)也是针对地球大气能量传输过程，提出了单位时间内熵增量最大的原则，他引用了Malkus和Veronis(1958)在流体力学方面的工作，"证明了一个最大热流的原则，而最大热流又是一个给定边界条件下的最大熵产"，但这个推论在逻辑上是不成立的。同样是研究行星大气动力学，Shutts(1981)采用与Paltridge不同的熵产定义方法，研究了一种更抽象的方法来检验最大熵产原则，并报告了良好的拟合度。

==Prospects==
前景展望

Until recently, prospects for useful extremal principles in this area have seemed clouded. C. Nicolis (1999) concludes that one model of atmospheric dynamics has an attractor which is not a regime of maximum or minimum dissipation; she says this seems to rule out the existence of a global organizing principle, and comments that this is to some extent disappointing; she also points to the difficulty of finding a thermodynamically consistent form of entropy production. Another top expert offers an extensive discussion of the possibilities for principles of extrema of entropy production and of dissipation of energy: Chapter 12 of Grandy (2008) and chemical reactions do not obey extremal principles for the secondary differential of entropy production, hence the development of a general extremal principle seems infeasible.

直到最近，这一领域有用的极值原则的前景似乎还不明朗。C.Nicolis(1999年)的结论是，一个大气动力学模型的吸引子不是最大或最小耗散的制度；她说，这似乎排除了全球组织原则的存在，并评论说，这在某种程度上令人失望；她还指出，很难找到热力学上一致的熵生产形式。另一位顶级专家则对熵的产生和能量耗散的极值原则的可能性进行了广泛的讨论。Grandy(2008年)第12章和化学反应不服从熵产生二次微分的极值原则，因此制定一个普遍的极值原则似乎是不可行的。

==See also==
* Non-equilibrium thermodynamics 非平衡热力学
* Dissipative system 耗散系统
* Self-organization 自组织
* Autocatalytic reactions and order creation 自动催化反应和秩序创造
* Fluctuation theorem涨落定理
* Fluctuation dissipation theorem波动耗散定理

==References==

<noinclude>

This page was moved from [[wikipedia:en:Extremal principles in non-equilibrium thermodynamics]]. Its edit history can be viewed at [[非平衡热力学的极值定理/edithistory]]</noinclude>

自催化

2020-12-25T09:27:26Z

Yetmings：

此词条暂由Henry 翻译。

{{more citations needed|date=September 2010}}

A single [[chemical reaction]] is said to be '''autocatalytic''' if one of the reaction products is also a [[catalyst]] for the same or a coupled reaction.<ref name=Steinfeld>Steinfeld J.I., Francisco J.S. and Hase W.L. ''Chemical Kinetics and Dynamics'' (2nd ed., Prentice-Hall 1999) p.151-2 {{ISBN|0-13-737123-3}}</ref> Such a reaction is called an '''autocatalytic reaction'''.

A single chemical reaction is said to be autocatalytic if one of the reaction products is also a catalyst for the same or a coupled reaction. Such a reaction is called an autocatalytic reaction.

一个单一的化学反应，如果其中一个反应产物也是同一反应或耦合反应的催化剂，则称为具有自催化性质。这种反应称为 自催化反应autocatalytic reaction。

A ''set'' of chemical reactions can be said to be "collectively autocatalytic" if a number of those reactions produce, as reaction products, catalysts for enough of the other reactions that the entire set of chemical reactions is self-sustaining given an input of energy and food molecules (see [[autocatalytic set]]).

A set of chemical reactions can be said to be "collectively autocatalytic" if a number of those reactions produce, as reaction products, catalysts for enough of the other reactions that the entire set of chemical reactions is self-sustaining given an input of energy and food molecules (see autocatalytic set).

如果一系列化学反应作为反应产物产生足够多的其他反应的催化剂，使整套化学反应在能量和食物分子输入的情况下能够自我维持，则可以说这些化学反应是”集体自催化”的。

==Chemical reactions化学反应==

{{main|Chemical reaction|Chemical kinetics}}

A chemical reaction of two reactants and two products can be written as

A chemical reaction of two reactants and two products can be written as

两种反应物和两种产物的化学反应可以写成

:<math> \alpha A + \beta B \rightleftharpoons \sigma S + \tau T</math>

<math> \alpha A + \beta B \rightleftharpoons \sigma S + \tau T</math>

where the Greek letters are [[stoichiometric coefficients]] and the capital Latin letters represent chemical species. The chemical reaction proceeds in both the forward and reverse direction. This equation is easily generalized to any number of reactants, products, and reactions.

where the Greek letters are stoichiometric coefficients and the capital Latin letters represent chemical species. The chemical reaction proceeds in both the forward and reverse direction. This equation is easily generalized to any number of reactants, products, and reactions.

其中希腊字母是化学计量系数，大写拉丁字母代表化学物种。化学反应在正向和反向两个方向进行。这个方程可以很容易地推广到任意数量的反应物、产物和反应。

===Chemical equilibrium化学平衡===

In [[chemical equilibrium]] the forward and reverse [[reaction rate]]s are such that each chemical species is being created at the same rate it is being destroyed. In other words, the rate of the forward reaction is equal to the rate of the reverse reaction.

In chemical equilibrium the forward and reverse reaction rates are such that each chemical species is being created at the same rate it is being destroyed. In other words, the rate of the forward reaction is equal to the rate of the reverse reaction.

在化学平衡状态，正向和反向的反应速率是这样的情况：每一种化学物质都以同样的速率生成和消失。换句话说，正向反应的速率等于反向反应的速率。

:<math> k_+ [ A ]^\alpha [B ]^\beta = k_{-} [S ]^\sigma[T ]^\tau \,</math>

<math> k_+ [ A ]^\alpha [B ]^\beta = k_{-} [S ]^\sigma[T ]^\tau \,</math>

K _ + [ a ] ^ alpha [ b ] ^ beta = k _ {-}[ s ] ^ sigma [ t ] ^ tau，</math >

Here, the brackets indicate the concentration of the chemical species, in [[mole (unit)|moles]] per liter, and k+ and k− are [[rate constant]]s.

Here, the brackets indicate the concentration of the chemical species, in moles per liter, and k+ and k− are rate constants.

这里，括号表示化学物质的浓度，以摩尔/升为单位，k+和 k-是速率常数。

===Far from equilibrium远离平衡态===

Far from equilibrium, the forward and reverse reaction rates no longer balance and the concentration of reactants and products is no longer constant. For every forward reaction <math>\alpha </math> molecules of A are destroyed. For every reverse reaction <math>\alpha </math> molecules of A are created. In the case of an [[elementary reaction]] step the [[reaction order]] in each direction equals the molecularity, so that the rate of change in the number of moles of A is then

Far from equilibrium, the forward and reverse reaction rates no longer balance and the concentration of reactants and products is no longer constant. For every forward reaction <math>\alpha </math> molecules of A are destroyed. For every reverse reaction <math>\alpha </math> molecules of A are created. In the case of an elementary reaction step the reaction order in each direction equals the molecularity, so that the rate of change in the number of moles of A is then

在远离平衡态时，正向和反向反应速率不再是平衡的，反应物和产物的浓度不再是恒定的。对于每一个前向反应，a 的分子会消失。对于每一个逆反应，a 的分子都会被产生出来。在基本反应步骤中，每个方向的反应级数等于“反应分子数”（molecularity），因此 a 的摩尔数的变化率就是

:<math>{d \over dt}[ A ] =-\alpha k_+ [ A ]^\alpha [B ]^\beta +\alpha k_{-} [S ]^\sigma[T ]^\tau \,</math>

<math>{d \over dt}[ A ] =-\alpha k_+ [ A ]^\alpha [B ]^\beta +\alpha k_{-} [S ]^\sigma[T ]^\tau \,</math>

[ a ] =-alpha k _ + [ a ] ^ alpha [ b ] ^ beta + alpha k _ {-}[ s ] ^ sigma [ t ] ^ tau，</math >

:<math>{d \over dt}[ B ] =-\beta k_+ [ A ]^\alpha [B ]^\beta +\beta k_{-} [S ]^\sigma[T ]^\tau \,</math>

<math>{d \over dt}[ B ] =-\beta k_+ [ A ]^\alpha [B ]^\beta +\beta k_{-} [S ]^\sigma[T ]^\tau \,</math>

[ b ] =-beta k _ + [ a ] ^ alpha [ b ] ^ beta + beta k _ {-}[ s ] ^ sigma [ t ] ^ tau，</math >

:<math>{d \over dt}[ S ] =\sigma k_+ [ A ]^\alpha [B ]^\beta -\sigma k_{-} [S ]^\sigma[T ]^\tau \,</math>

<math>{d \over dt}[ S ] =\sigma k_+ [ A ]^\alpha [B ]^\beta -\sigma k_{-} [S ]^\sigma[T ]^\tau \,</math>

[ s ] = sigma k _ + [ a ] ^ alpha [ b ] ^ beta-sigma k _ {-}[ s ] ^ sigma [ t ] ^ tau，</math >

:<math>{d \over dt}[ T ] =\tau k_+ [ A ]^\alpha [B ]^\beta -\tau k_{-} [S ]^\sigma[T ]^\tau \,</math>

<math>{d \over dt}[ T ] =\tau k_+ [ A ]^\alpha [B ]^\beta -\tau k_{-} [S ]^\sigma[T ]^\tau \,</math>

[ t ] = tau k _ + [ a ] ^ alpha [ b ] ^ beta-tau k _ {-}[ s ] ^ sigma [ t ] ^ tau，</math >

This system of equations has a single stable [[Fixed point (mathematics)|fixed point]] when the forward rates and the reverse rates are equal (when <math>{d \over dt}=0</math> for every species). This means that the system evolves to the equilibrium state, and this is the only state to which it evolves.<ref>{{cite journal |last1=Ross |first1=John |last2=Garcia-Colin |first2=Leopoldo S. |title=Thermodynamics of chemical systems far from equilibrium |journal=The Journal of Physical Chemistry |date=March 1989 |volume=93 |issue=5 |pages=2091–2092 |doi=10.1021/j100342a075}}</ref>

This system of equations has a single stable fixed point when the forward rates and the reverse rates are equal (when <math>{d \over dt}=0</math> for every species). This means that the system evolves to the equilibrium state, and this is the only state to which it evolves.

这个系统的方程组有一个单一的稳定不动点解，这个解的情况就是每个物种的正向速率和反向速率相等。这意味着这个系统是往平衡状态演化，而且这个平衡状态这是系统演化到的唯一状态。

===Autocatalytic reactions自催化反应===

[[Image:Sigmoid curve for an autocatalytical reaction.jpg|256px|right|thumb|Sigmoid variation of product concentration in autocatalytic reactions]]

Sigmoid variation of product concentration in autocatalytic reactions

自催化反应中产物浓度的 s 形变化

Autocatalytic reactions are those in which at least one of the products is a reactant. Perhaps the simplest autocatalytic reaction can be written<ref name=Steinfeld/>

Autocatalytic reactions are those in which at least one of the products is a reactant. Perhaps the simplest autocatalytic reaction can be written

自催化反应是那些其中至少一个产物是反应物的反应。最简单的自催化反应可以是这样的形式

:<math> A + B \rightleftharpoons 2B</math>

<math>[A]=\frac{[A]_0+[B]_0}{1+\frac{[B]_0}{[A]_0}e^{([A]_0+[B]_0)kt}}</math>

< math > [ a ] = frac {[ a ] _ 0 + [ b ] _ 0}{1 + frac {[ b ] _ 0}{[ a ] _ 0} e ^ {(([ a ] _ 0 + [ b ] _ 0) kt }} </math >

and

及

with the rate equations (for an elementary reaction)

<math>[B]=\frac{[A]_0+[B]_0}{1+\frac{[A]_0}{[B]_0}e^{-([A]_0+[B]_0)kt}}</math>.

< math > [ b ] = frac {[ a ] _ 0 + [ b ] _ 0}{1 + frac {[ a ] _ 0}{[ b ] _ 0} e ^ {-([ a ] _ 0 + [ b ] _ 0) kt }} </math > .

:<math>{d \over dt}[ A ] =- k_+ [ A ] [B ] + k_{-} [B ]^2 \,</math>

The graph for these equations is a sigmoid curve (specifically a logistic function), which is typical for autocatalytic reactions: these chemical reactions proceed slowly at the start (the induction period) because there is little catalyst present, the rate of reaction increases progressively as the reaction proceeds as the amount of catalyst increases and then it again slows down as the reactant concentration decreases. If the concentration of a reactant or product in an experiment follows a sigmoid curve, the reaction may be autocatalytic.

这些方程的曲线图是一条s形曲线（特别是logistic函数），这是自催化反应的典型特征：这些化学反应在开始时（诱导期）进行得很慢，因为几乎没有催化剂存在，随着催化剂用量的增加，反应速度逐渐增加，然后随着反应物浓度的降低，反应速度再次减慢。如果一个实验中反应物或产物的浓度服从s形曲线，则该反应可能是自催化的。

:<math>{d \over dt}[ B ] = + k_+ [ A ] [B ] -k_{-} [B ]^2 \,</math>.

These kinetic equations apply for example to the acid-catalyzed hydrolysis of some esters to carboxylic acids and alcohols. In the hurricane example, hurricanes are formed from unequal heating within the atmosphere. The Earth's atmosphere is then far from thermal equilibrium. The order of the Earth's atmosphere increases, but at the expense of the order of the sun. The sun is becoming more disorderly as it ages and throws off light and material to the rest of the universe. The total disorder of the sun and the earth increases despite the fact that orderly hurricanes are generated on earth.

这些动力学方程适用于一些酯的酸催化水解为羧酸和醇。在飓风的例子中，飓风是由大气中不均匀的加热形成的。地球的大气层离热平衡还很远。地球大气的秩序增加了，但以太阳的秩序为代价。随着年龄的增长，太阳正变得越来越无序，并向宇宙的其他部分发射光和物质。尽管有秩序的飓风随时都会发生，但太阳和地球的整体混乱程度却在增加。

This reaction is one in which a molecule of species A interacts with a molecule of species B. The A molecule is converted into a B molecule. The final product consists of the original B molecule plus the B molecule created in the reaction.

这个反应是物种A的分子与物种B的分子相互作用，A分子转化为B分子。最终产物由原始的B分子加上反应中产生的B分子组成。

A similar example exists for living chemical systems. The sun provides energy to green plants. The green plants are food for other living chemical systems. The energy absorbed by plants and converted into chemical energy generates a system on earth that is orderly and far from chemical equilibrium. Here, the difference from chemical equilibrium is determined by an excess of reactants over the equilibrium amount. Once again, order on earth is generated at the expense of entropy increase of the sun. The total entropy of the earth and the rest of the universe increases, consistent with the Second Law.

类似的例子也存在于活的化学系统中。太阳为绿色植物提供能量。绿色植物是其他生命化学系统的食物。植物吸收并转化为化学能的能量在地球上形成了一个有序的系统，这个系统远离化学平衡。在这里，反应物超过平衡量决定了化学平衡的差异。再一次，地球上的秩序是以太阳的熵增为代价而产生的。地球和宇宙其余部分的总熵增加，符合第二定律。

The key feature of these rate equations is that they are [[nonlinear]]; the second term on the right varies as the square of the concentration of B. This feature can lead to multiple fixed points of the system, much like a [[quadratic equation]] can have multiple roots. Multiple fixed points allow for multiple states of the system. A system existing in multiple [[macroscopic]] states is more orderly (has lower entropy) than a system in a single state.
这些速率方程的关键特征是它们是[[非线性]；右边的第二项随B浓度的平方而变化。这一特性可导致系统的多个不动点，就像[[二次方程]]可以有多个根一样。多个固定点允许系统的多种状态。存在于多个[[宏观]]状态的系统比处于单一状态的系统更有序（熵更低）。

Some autocatalytic reactions also generate order in a system at the expense of its surroundings. For example, (clock reactions) have intermediates whose concentrations oscillate in time, corresponding to temporal order. Other reactions generate spatial separation of chemical species corresponding to spatial order. More complex reactions are involved in metabolic pathways and metabolic networks in biological systems.

一些自催化反应也以牺牲周围环境为代价，在系统中产生有序。例如，(时钟反应)有其浓度在时间上振荡的中间体，对应于时间顺序。其他反应产生空间分离的化学物质对应的空间秩序。更复杂的反应涉及到生物系统中的代谢途径和代谢网络。

The concentrations of A and B vary in time according to<ref name=Steinfeld/><ref name=Moore>Moore J.W. and [[Ralph Pearson|Pearson R.G.]] ''Kinetics and Mechanism'' (John Wiley 1981) p.26 {{ISBN|0-471-03558-0}}</ref>

:<math>[A]=\frac{[A]_0+[B]_0}{1+\frac{[B]_0}{[A]_0}e^{([A]_0+[B]_0)kt}}</math>

The transition to order as the distance from equilibrium increases is not usually continuous. Order typically appears abruptly. The threshold between the disorder of chemical equilibrium and order is known as a phase transition. The conditions for a phase transition can be determined with the mathematical machinery of non-equilibrium thermodynamics.

随着离平衡距离的增加，向有序的过渡通常是不连续的。秩序通常会突然出现。化学平衡和有序之间的无序阈值被称为相变。相变的条件可以用非平衡态热力学的数学方法来确定。

and

:<math>[B]=\frac{[A]_0+[B]_0}{1+\frac{[A]_0}{[B]_0}e^{-([A]_0+[B]_0)kt}}</math>.

The graph for these equations is a [[sigmoid function|sigmoid curve]] (specifically a [[logistic function]]), which is typical for autocatalytic reactions: these chemical reactions proceed slowly at the start (the [[induction period]]) because there is little catalyst present, the rate of reaction increases progressively as the reaction proceeds as the amount of catalyst increases and then it again slows down as the reactant concentration decreases. If the concentration of a reactant or product in an experiment follows a sigmoid curve, the reaction may be autocatalytic.
这些方程的图形是一个[[西格莫函数| S形曲线]]（特别是[[逻辑函数]]），这是自催化反应的典型特征：这些化学反应在开始时（诱导期]]）进行得很慢，因为催化剂很少，随着催化剂用量的增加，反应速度逐渐增加，然后随着反应物浓度的降低，反应速度再次减慢。如果一个实验中反应物或产物的浓度服从sigmoid曲线，则该反应可能是自催化的。
A chemical reaction cannot oscillate about a position of final equilibrium because the second law of thermodynamics requires that a thermodynamic system approach equilibrium and not recede from it. For a closed system at constant temperature and pressure, the Gibbs free energy must decrease continuously and not oscillate. However it is possible that the concentrations of some reaction intermediates oscillate, and also that the rate of formation of products oscillates.

一个化学反应不能在一个最终平衡位置上振荡，因为热力学第二定律需要一个接近平衡的热力学系统，而不能退出平衡位置。对于一个温度和压力恒定的封闭系统， 吉布斯自由能Gibbs free energy必须不断减小而不振荡。然而，一些反应中间体的浓度可能会振荡，产物的生成速率也可能振荡。

These kinetic equations apply for example to the acid-catalyzed hydrolysis of some [[ester]]s to [[carboxylic acid]]s and [[alcohol]]s.<ref name=Moore/> There must be at least some acid present initially to start the catalyzed mechanism; if not the reaction must start by an alternate uncatalyzed path which is usually slower. The above equations for the catalyzed mechanism would imply that the concentration of acid product remains zero forever.<ref name=Moore/>
例如，这些动力学方程适用于某些[[酯]]到[[羧酸]]和[[醇]]的酸催化水解。最初必须至少存在一些酸来启动催化机制；否则，反应必须通过通常较慢的替代非催化路径开始。上述催化机理的方程式意味着酸产物的浓度永远为零。

The Lotka–Volterra equation is [[isomorphic with the predator–prey model and the two-reaction autocatalytic model. In this example baboons and cheetahs are equivalent to two different chemical species X and Y in autocatalytic reactions.]]

方程[同构于捕食-食饵模型和双反应自催化模型。在这个例子中，狒狒和猎豹在自动催化反应中相当于两种不同的化学物种 x 和 y

==Creation of order秩序创立==

Consider a coupled set of two autocatalytic reactions in which the concentration of one of the reactants A is much larger than its equilibrium value. In this case, the forward reaction rate is so much larger than the reverse rates that we can neglect the reverse rates.

考虑一组耦合的两个自催化反应，其中一个反应物 a 的浓度远远大于其平衡值。在这种情况下，正向反应速率远远大于反向反应速率，因此我们可以忽略反向反应速率。

===Background背景===

<math> A + X \rightarrow 2X</math>

A + x 右行2X

The [[second law of thermodynamics]] states that the disorder ([[entropy]]) of a physical or chemical system and its surroundings (a [[closed system]]) must increase with time. Systems left to themselves become increasingly [[random]], and orderly energy of a system like uniform motion degrades eventually to the random motion of particles in a [[heat bath]].
[[热力学第二定律]指出，物理或化学系统及其周围环境（封闭系统）的无序度（[[熵]]）必须随时间而增加。留给自己的系统变得越来越[[随机]]，系统的有序能量（如均匀运动）最终退化为粒子在[[热浴]中的随机运动
<math> X + Y \rightarrow 2Y</math>

(数学) x + y 右行2Y

There are, however, many instances in which physical systems spontaneously become [[emergence|emergent]] or orderly. For example, despite the destruction they cause, [[hurricane]]s have a very orderly [[vortex]] motion when compared to the random motion of the air molecules in a closed room. Even more spectacular is the order created by chemical systems; the most dramatic being the order associated with life.
然而，在许多情况下，物理系统自发地变得新生或有序。例如，尽管飓风造成了破坏，但与封闭房间中空气分子的随机运动相比，[[飓风]]的运动非常有序。更引人注目的是化学系统创造的秩序；最引人注目的是与生命相关的秩序。
<math> Y \rightarrow E</math>

[数学，数学]

This is consistent with the Second Law, which requires that the total disorder of a system ''and its surroundings'' must increase with time. Order can be created in a system by an even greater decrease in order of the system's surroundings.<ref>{{cite book | author=Ilya Prigogine | title=From Being to Becoming: Time and Complexity in the Physical Sciences | location=San Francisco | publisher=W. H. Freeman | year=1980 | isbn=978-0-7167-1107-0 | author-link=Ilya Prigogine | url-access=registration | url=https://archive.org/details/frombeingtobecom00ipri }}
这与第二定律是一致的，第二定律要求系统“及其周围环境”的整体无序程度必须随时间而增加。在一个系统中，秩序可以通过系统周围环境的更大程度的降低而产生
with the rate equations

用速率方程式

</ref> In the hurricane example, hurricanes are formed from unequal heating within the atmosphere. The Earth's atmosphere is then far from [[thermal equilibrium]]. The order of the Earth's atmosphere increases, but at the expense of the order of the sun. The sun is becoming more disorderly as it ages and throws off light and material to the rest of the universe. The total disorder of the sun and the earth increases despite the fact that orderly hurricanes are generated on earth.

在飓风的例子中，飓风是由大气中不均匀的加热形成的。地球的大气层离[[热平衡]]很远。地球大气的秩序增加了，但以太阳的秩序为代价。随着年龄的增长，太阳正变得越来越无序，并向宇宙的其他部分发射光和物质。尽管地球上产生了有序的飓风，但太阳和地球的总体混乱程度却在增加。

<math>{d \over dt}[ X ] = k_1 [ A ] [X ] - k_{2} [X ][Y ] \,</math>

< math > { d over dt }[ x ] = k_1[ a ][ x ]-k_2}[ x ][ y ] ，</math >

A similar example exists for living chemical systems. The sun provides energy to green plants. The green plants are food for other living chemical systems. The energy absorbed by plants and converted into chemical energy generates a system on earth that is orderly and far from [[chemical equilibrium]]. Here, the difference from chemical equilibrium is determined by an excess of reactants over the equilibrium amount. Once again, order on earth is generated at the expense of entropy increase of the sun. The total entropy of the earth and the rest of the universe increases, consistent with the Second Law.

生命化学系统也有类似的例子。太阳为绿色植物提供能量。绿色植物是其他生物化学系统的食物。被植物吸收并转化为化学能的能量在地球上产生了一个有序的、远离[化学平衡]的系统。在这里，与化学平衡的差异是由反应物超过平衡量所决定的。地球上的秩序再一次以太阳的熵增加为代价。地球和宇宙其他部分的总熵增加，符合第二定律

<math>{d \over dt}[ Y ] = k_2 [ X ] [Y ] - k_{3} [Y ] \,</math>.

[ y ] = k _ 2[ x ][ y ]-k _ {3}[ y ] ，[/math ].

Some autocatalytic reactions also generate order in a system at the expense of its surroundings. For example, ([[clock reactions]]) have [[reaction intermediate|intermediates]] whose concentrations oscillate in time, corresponding to temporal order. Other reactions generate spatial separation of [[chemical species]] corresponding to spatial order. More complex reactions are involved in [[metabolic pathway]]s and [[metabolic network]]s in [[biological systems]].
一些自催化反应也以牺牲周围环境为代价在系统中产生秩序。例如，（[[时钟反应]]）有[[反应中间体|中间体]]，其浓度随时间振荡，与时间顺序相对应。其他反应产生空间分离[[化学物种]]对应的空间顺序。在[[生物系统]]中的[[代谢途径]]s和[[代谢网络]]涉及更复杂的反应

Here, we have neglected the depletion of the reactant A, since its concentration is so large. The rate constants for the three reactions are <math>k_1</math>, <math>k_2</math>, and <math>k_3</math>, respectively.

在这里，我们忽略了反应物 a 的耗尽，因为它的浓度很大。这三个反应的速率常数分别是k1,k2,k3 。

The transition to order as the distance from equilibrium increases is not usually continuous. Order typically appears abruptly. The threshold between the disorder of chemical equilibrium and order is known as a [[phase transition]]. The conditions for a phase transition can be determined with the mathematical machinery of [[non-equilibrium thermodynamics]].

随着与平衡的距离增加，向有序的转变通常不是连续的。顺序通常会突然出现。化学平衡与有序之间的界限称为[[相变]]。相变的条件可以用[[非平衡态热力学]的数学机制来确定

This system of rate equations is known as the Lotka–Volterra equation and is most closely associated with population dynamics in predator–prey relationships. This system of equations can yield oscillating concentrations of the reaction intermediates X and Y. The amplitude of the oscillations depends on the concentration of A (which decreases without oscillation). Such oscillations are a form of emergent temporal order that is not present in equilibrium.

这个速率方程组被称为 Lotka-Volterra 方程，在捕食者-食饵关系中与族群动态最密切相关。这个方程组可以产生反应中间体 x 和 y 的振荡浓度。振荡的振幅取决于 a 的浓度(a 的浓度下降而没有振荡)。这种振荡是一种涌现的时间顺序，在平衡中不存在。

===Temporal order时间顺序===

A chemical reaction cannot oscillate about a position of final [[chemical equilibrium|equilibrium]] because the second law of thermodynamics requires that a [[thermodynamic system]] approach equilibrium and not recede from it. For a closed system at constant temperature and pressure, the [[Gibbs free energy]] must decrease continuously and not oscillate. However it is possible that the concentrations of some [[reaction intermediate]]s oscillate, and also that the ''rate'' of formation of products oscillates.<ref>Espenson, J.H. ''Chemical Kinetics and Reaction Mechanisms'' (2nd ed., McGraw-Hill 2002) p.190 {{ISBN|0-07-288362-6}}</ref>
一个化学反应不能围绕最终的[[化学平衡|平衡]]的位置振荡，因为热力学第二定律要求[[热力学系统]]接近平衡，而不是从中退却。对于一个恒温恒压的封闭系统，[[Gibbs自由能]必须连续下降而不振荡。然而，一些[[反应中间体]]的浓度可能会振荡，产物形成的“速率”也会振荡。

====Idealized example: Lotka–Volterra equation理想化例子：Lotka–Volterra 等式====

Another example of a system that demonstrates temporal order is the Brusselator (see Prigogine reference). It is characterized by the reactions

另一个演示时间顺序的系统例子是 Brusselator (见 Prigogine 参考文献)。人们的反应是拥有属性的

[[File:CentralTendencyLV.jpg|thumb|right|350px|The Lotka–Volterra equation is [[isomorphic]] with the predator–prey model and the two-reaction autocatalytic model. In this example baboons and cheetahs are equivalent to two different chemical species X and Y in autocatalytic reactions.]]

Consider a coupled set of two autocatalytic reactions in which the concentration of one of the reactants A is much larger than its equilibrium value. In this case, the forward reaction rate is so much larger than the reverse rates that we can neglect the reverse rates.
考虑一组耦合的两个自催化反应，其中一个反应物a的浓度远远大于其平衡值。在这种情况下，正向反应速率比反向速率大得多，我们可以忽略反向速率。
<math> A \rightarrow X</math>

《数学》 a right tarrow x

:<math> A + X \rightarrow 2X</math>

<math> 2X + Y \rightarrow 3X</math>

2X + y 右行3X

:<math> X + Y \rightarrow 2Y</math>

<math> B + X \rightarrow Y + D</math>

B + x 右边 y + d

:<math> Y \rightarrow E</math>

<math> X \rightarrow E</math>

X 右边的 e

with the rate equations

with the rate equations

用速率方程式

:<math>{d \over dt}[ X ] = k_1 [ A ] [X ] - k_{2} [X ][Y ] \,</math>

<math>{d \over dt}[ X ] = [A ] + [ X ]^2 [Y ] - [B ] [X ] - [X ] \,</math>

< math > { d over dt }[ x ] = [ a ] + [ x ] ^ 2[ y ]-[ b ][ x ]-[ x ] ，</math >

:<math>{d \over dt}[ Y ] = k_2 [ X ] [Y ] - k_{3} [Y ] \,</math>.

<math>{d \over dt}[ Y ] = [B ] [X ] - [ X ]^2 [Y ] \,</math>

[数学]{ d/dt }[ y ] = [ b ][ x ]-[ x ] ^ 2[ y ] ，[/math ]

Here, we have neglected the depletion of the reactant A, since its concentration is so large. The rate constants for the three reactions are <math>k_1</math>, <math>k_2</math>, and <math>k_3</math>, respectively.

where, for convenience, the rate constants have been set to 1.

为了方便起见，速率常数设置为1。

This system of rate equations is known as the [[Lotka–Volterra equation]] and is most closely associated with [[population dynamics]] in predator–prey relationships. This system of equations can yield oscillating concentrations of the reaction intermediates X and Y. The amplitude of the oscillations depends on the concentration of A (which decreases without oscillation). Such oscillations are a form of emergent temporal order that is not present in equilibrium.
这个速率方程组被称为[[Lotka–Volterra equation]]，在捕食者-猎物关系中与[[种群动力学]]联系最为密切。这个方程组可以得到反应中间体X和Y的振荡浓度，振荡的幅度取决于A的浓度（A的浓度减少而不振荡）。这种振荡是一种在平衡状态下不存在的突发时序形式。
The Brusselator in the unstable regime. A=1. B=2.5. X(0)=1. Y(0)=0. The system approaches a [[limit cycle. For B<1+A the system is stable and approaches a fixed point.]]

不稳定政权中的布鲁塞尔振子。 A=1. B=2.5. X(0)=1. Y(0)=0.该系统接近[极限环]。对于 b < 1 + a，系统是稳定的，并且接近一个固定点。]

The Brusselator has a fixed point at

布鲁塞尔振子有一个固定点

====Another idealized example: Brusselator另一个理想化模型：布鲁塞尔振子====

<math>[ X ] = A \,</math>

[数学] = a，[数学]

Another example of a system that demonstrates temporal order is the [[Brusselator]] (see Prigogine reference). It is characterized by the reactions

<math>[ Y ] = {B \over A} \,</math>.

[ math ][ y ] = { b over a } ，[ math ].

:<math> A \rightarrow X</math>

The fixed point becomes unstable when

定点变得不稳定，当

:<math> 2X + Y \rightarrow 3X</math>

<math> B>1+A^2 \,</math>

1 + a ^ 2,

:<math> B + X \rightarrow Y + D</math>

leading to an oscillation of the system. Unlike the Lotka-Volterra equation, the oscillations of the Brusselator do not depend on the amount of reactant present initially. Instead, after sufficient time, the oscillations approach a limit cycle.

导致了系统的振荡。与Lotka-Volterra 方程不同，布鲁塞尔振荡器的振荡并不取决于最初反应物的数量。相反，在足够的时间之后，振荡接近极限环。

:<math> X \rightarrow E</math>

with the rate equations

An idealized example of spatial spontaneous symmetry breaking is the case in which we have two boxes of material separated by a permeable membrane so that material can diffuse between the two boxes. It is assumed that identical Brusselators are in each box with nearly identical initial conditions. (see Prigogine reference)

一个理想化的空间自发对称性破缺的例子是，我们有两个盒子的材料被一个可渗透的薄膜分开，这样材料可以在两个盒子之间扩散。我们假设在每个盒子中都有相同的布鲁塞尔振子，并且具有几乎相同的初始条件。(见 Prigogine 参考文献)

:<math>{d \over dt}[ X ] = [A ] + [ X ]^2 [Y ] - [B ] [X ] - [X ] \,</math>

<math>{d \over dt}[ X_1 ] = [A ] + [ X _1]^2 [Y_1 ] - [B ] [X_1 ] - [X_1 ] + D_x\left( X_2 - X_1 \right)\,</math>

< math > { d over dt }[ x _ 1] = [ a ] + [ x _ 1] ^ 2[ y _ 1]-[ b ][ x _ 1]-[ x _ 1] + d _ x 左(x _ 2-x _ 1右) ，</math >

:<math>{d \over dt}[ Y ] = [B ] [X ] - [ X ]^2 [Y ] \,</math>

<math>{d \over dt}[ Y_1 ] = [B ] [X_1 ] - [ X_1 ]^2 [Y_1 ] + D_y\left( Y_2 - Y_1\right) \,</math>

< math > { d over dt }[ y _ 1] = [ b ][ x _ 1]-[ x _ 1] ^ 2[ y _ 1] + d _ y 左(y _ 2-y _ 1右) ，</math >

where, for convenience, the rate constants have been set to 1.
其中，为了方便起见，速率常数被设置为1。
<math>{d \over dt}[ X_2 ] = [A ] + [ X _2]^2 [Y_2 ] - [B ] [X_2 ] - [X_2 ] + D_x\left( X_1 - X_2 \right)\,</math>

[ x _ 2] = [ a ] + [ x _ 2] ^ 2[ y _ 2]-[ b ][ x _ 2]-[ x _ 2] + d _ x 左(x _ 1-x _ 2右) ，</math >

[[File:080205 Brusselator picture.jpg|thumb|right|350px|The Brusselator in the unstable regime. A=1. B=2.5. X(0)=1. Y(0)=0. The system approaches a [[limit cycle]]. For B<1+A the system is stable and approaches a [[Fixed point (mathematics)|fixed point]].]]

<math>{d \over dt}[ Y_2 ] = [B ] [X_2 ] - [ X_2 ]^2 [Y_2 ] + D_y\left( Y_1 - Y_2\right) \,</math>

[ math ]{ d over dt }[ y _ 2] = [ b ][ x _ 2]-[ x _ 2] ^ 2[ y _ 2] + d _ y 左(y _ 1-y _ 2右) ，</math >

The Brusselator has a fixed point at
布鲁塞尔振子有一个固定点在

Here, the numerical subscripts indicate which box the material is in. There are additional terms proportional to the diffusion coefficient D that account for the exchange of material between boxes.

在这里，数字下标表示材料在哪个盒子里。还有一些与扩散系数 d 成比例的附加项，用于解释盒子之间的物质交换。

:<math>[ X ] = A \,</math>

If the system is initiated with the same conditions in each box, then a small fluctuation will lead to separation of materials between the two boxes. One box will have a predominance of X, and the other will have a predominance of Y.

如果系统启动时每个盒子的条件相同，那么一个小的波动将导致两个盒子之间的物料分离。一个盒子将具有 x 的优势，而另一个盒子将具有 y 的优势。

:<math>[ Y ] = {B \over A} \,</math>.

The fixed point becomes unstable when

固定点变得不稳定当

Real examples of clock reactions are the Belousov–Zhabotinsky reaction (BZ reaction), the Briggs–Rauscher reaction, the Bray–Liebhafsky reaction and the iodine clock reaction. These are oscillatory reactions, and the concentration of products and reactants can be approximated in terms of damped oscillations.

时钟反应的真实例子是 Belousov-Zhabotinsky 反应(BZ 反应) ，Briggs-Rauscher 反应，Bray-Liebhafsky 反应和碘钟反应。这些都是振荡反应，产物和反应物的浓度可以用阻尼振荡来近似。

:<math> B>1+A^2 \,</math>

The best-known reaction, the BZ reaction, can be created with a mixture of potassium bromate <chem>(KBrO3)</chem>, malonic acid <chem>(CH2(COOH)2)</chem>, and manganese sulfate <chem>(MnSO4)</chem> prepared in a heated solution with sulfuric acid <chem>(H2SO4)</chem> as solvent.

其中最著名的反应是 BZ 反应，它是在硫酸 </chem > (H2SO4) </chem > (H2SO4) </chem > (CH2(COOH)2) </chem > 和用硫酸 </chem > (MnSO4) </chem > 加热溶液中制得的混合溴酸钾。

leading to an oscillation of the system. Unlike the Lotka-Volterra equation, the oscillations of the Brusselator do not depend on the amount of reactant present initially. Instead, after sufficient time, the oscillations approach a [[limit cycle]].<ref>{{cite web

|url=http://www.math.ohio-state.edu/~ault/Papers/Brusselator.pdf

|title=Archived copy

Another autocatalytic system is one driven by light coupled to photo-polymerization reactions. In a process termed optical autocatalysis, positive feedback is created between light intensity and photo-polymerization rate, via polymerization-induced increases in the refractive index. Light's preference to occupy regions of higher refractive index results in leakage of light into regions of higher molecular weight, thereby amplifying the photo-chemical reaction. The positive feedback may be expressed as:

另一种自催化体系是由光与光聚合反应耦合驱动的体系。在一个被称为光学自催化的过程中，光强度和光聚合速率之间产生正反馈，通过聚合诱导增加折射率。光喜欢占据折射率较高的区域，导致光线泄漏到分子量较高的区域，从而放大了光化学反应。积极的反馈可以表示为:

|accessdate=2015-10-15

|url-status=dead

<math>\text{polymerization rate} \to \text{molecular weight}/\text{refractive index} \to \text{intensity}</math>

文本{分子量}/文本{折射率}到文本{密度}

|archiveurl=https://web.archive.org/web/20081217020941/http://www.math.ohio-state.edu/~ault/Papers/Brusselator.pdf

|archivedate=2008-12-17

Noting that photo-polymerization rate is proportional to intensity and that refractive index is proportional to molecular weight, the positive feedback between intensity and photo-polymerization establishes the auto-catalytic behavior. Optical auto-catalysis has been shown to result on spontaneous pattern formation in photopolymers. Hosein and co-workers discovered that optical autocatalysis can also occur in photoreactive polymer blends, and that the process can induce binary phase morphologies with the same pattern as the light profile. Glycolysis consists of the degradation of one molecule of glucose and the overall production of two molecules of ATP. The process is therefore of great importance to the energetics of living cells. The global glycolysis reaction involves glucose, ADP, NAD, pyruvate, ATP, and NADH.

注意到光聚合速率与强度成正比，折射率与分子量成正比，强度与光聚合之间的正反馈建立了自催化行为。光学自催化已被证明是光聚合物自发形成图案的原因。Hosein和他的合作者发现，光学自催化也可以发生在光反应聚合物共混物中，这一过程可以诱导形成与光型相同的二元相形态。糖酵解是由一个葡萄糖分子的降解和两个 ATP 分子的全部产生组成。因此，这个过程对活细胞的能量学来说是非常重要的。糖酵解反应包括葡萄糖、 ADP、 NAD、丙酮酸、 ATP 和 NADH。

}} Dynamics of the Brusselator

</ref>

<chem>glucose{} + 2ADP{} + 2P_\mathit{i}{} + 2NAD -> 2(pyruvate){} + 2ATP{} + 2NADH</chem>.

< chem > glucose {} + 2ADP {} + 2P _ mathit { i }{} + 2NAD-> 2(丙酮酸盐){} + 2ATP {} + 2NADH </chem > 。

===Spatial order空间秩序===

The details of the process are quite involved, however, a section of the process is autocatalyzed by phosphofructokinase (PFK). This portion of the process is responsible for oscillations in the pathway that lead to the process oscillating between an active and an inactive form. Thus, the autocatalytic reaction can modulate the process.

该过程的细节相当复杂，然而，该过程的一部分是由磷酸果糖激酶(PFK)自催化的。这部分的过程负责振荡的路径，导致过程之间的振荡活跃和非活跃的形式。因此，自催化反应可以调节这一过程。

An idealized example of spatial [[spontaneous symmetry breaking]] is the case in which we have two boxes of material separated by a permeable membrane so that material can [[diffusion|diffuse]] between the two boxes. It is assumed that identical Brusselators are in each box with nearly identical initial conditions. (see Prigogine reference)

:<math>{d \over dt}[ X_1 ] = [A ] + [ X _1]^2 [Y_1 ] - [B ] [X_1 ] - [X_1 ] + D_x\left( X_2 - X_1 \right)\,</math>

It is possible to use the results from an autocatalytic reaction coupled with reaction–diffusion system theory to tailor the design of a thin layer. The autocatalytic process allows controlling the nonlinear behavior of the oxidation front, which is used to establish the initial geometry needed to generate the arbitrary final geometry. It has been successfully done in the wet oxidation of <math>Al_xGa_{1-x}As</math> to obtain arbitrary shaped layers of <math>AlO_x</math>.

利用自催化反应结合反应扩散系统理论的结果来设计薄层是可能的。自催化过程允许控制氧化前沿的非线性行为，用于建立生成任意最终几何所需的初始几何。在湿式氧化法中，成功地获得了任意形状的氧化铝层。

:<math>{d \over dt}[ Y_1 ] = [B ] [X_1 ] - [ X_1 ]^2 [Y_1 ] + D_y\left( Y_2 - Y_1\right) \,</math>

:<math>{d \over dt}[ X_2 ] = [A ] + [ X _2]^2 [Y_2 ] - [B ] [X_2 ] - [X_2 ] + D_x\left( X_1 - X_2 \right)\,</math>

The initial amounts of reactants determine the distance from a chemical equilibrium of the system. The greater the initial concentrations the further the system is from equilibrium. As the initial concentration increases, an abrupt change in order occurs. This abrupt change is known as phase transition. At the phase transition, fluctuations in macroscopic quantities, such as chemical concentrations, increase as the system oscillates between the more ordered state (lower entropy, such as ice) and the more disordered state (higher entropy, such as liquid water). Also, at the phase transition, macroscopic equations, such as the rate equations, fail. Rate equations can be derived from microscopic considerations. The derivations typically rely on a mean field theory approximation to microscopic dynamical equations. Mean field theory breaks down in the presence of large fluctuations (see Mean field theory article for a discussion). Therefore, since large fluctuations occur in the neighborhood of a phase transition, macroscopic equations, such as rate equations, fail. As the initial concentration increases further, the system settles into an ordered state in which fluctuations are again small. (see Prigogine reference)

反应物的初始量决定了与体系化学平衡的距离。初始浓度越大，系统离平衡越远。随着初始浓度的增加，顺序发生突变。这种突变被称为相变。在相变阶段，宏观量的波动，如化学浓度，随着系统在更有序的状态（低熵，如冰）和更无序的状态（更高的熵，如液态水）之间振荡而增加。同样，在相变过程中，宏观方程，如速率方程，会失效。速率方程可以从微观角度推导出来。推导通常依赖于对微观动力学方程的平均场理论近似。平均场理论在大波动的存在下会崩溃（见平均场理论文章的讨论）。因此，由于大的波动发生在相变附近，例如速率方程等的宏观方程便失灵了。随着初始浓度的进一步增加，系统进入有序状态，在这种状态下波动又很小(见 Prigogine 参考文献)

:<math>{d \over dt}[ Y_2 ] = [B ] [X_2 ] - [ X_2 ]^2 [Y_2 ] + D_y\left( Y_1 - Y_2\right) \,</math>

Here, the numerical subscripts indicate which box the material is in. There are additional terms proportional to the diffusion coefficient D that account for the exchange of material between boxes.

在这里，数字下标表示材料在哪个盒子里。还有一些与扩散系数D成比例的附加项，它们解释了盒子之间的物质交换。

Asymmetric autocatalysis occurs when the reaction product is chiral and thus acts as a chiral catalyst for its own production. Reactions of this type, such as the Soai reaction, have the property that they can amplify a very small enantiomeric excess into a large one. This has been proposed as an important step in the origin of biological homochirality.

不对称自催化反应发生在反应产物是手性的情况下，因此可以作为手性催化剂自身生产。这种类型的反应，比如 Soai 反应，具有将非常小的对映体过量百分数放大成大的反应的特性。这被认为是生物同手性起源的重要步骤。

If the system is initiated with the same conditions in each box, then a small fluctuation will lead to separation of materials between the two boxes. One box will have a predominance of X, and the other will have a predominance of Y.
如果系统在每个箱子的相同条件下启动，那么小的波动将导致两个箱子之间的物料分离。一个方框的优势是X，另一个方框的优势是Y。

==Real examples实例==

Real examples of [[clock reaction]]s are the [[Belousov–Zhabotinsky reaction]] (BZ reaction), the [[Briggs–Rauscher reaction]], the [[Bray–Liebhafsky reaction]] and the [[iodine clock reaction]]. These are oscillatory reactions, and the concentration of products and reactants can be approximated in terms of [[damping|damped]] [[oscillation]]s.
时钟反应]]的真正例子是[[Belousov–Zhabotinsky reaction]]（BZ反应）、[[Briggs–Rauscher 反应]]、[[Bray–Liebhafsky 反应]]和[[碘钟反应]]。这些都是振荡反应，产物和反应物的浓度可以用阻尼，振荡来近似。
In 1995 Stuart Kauffman proposed that life initially arose as autocatalytic chemical networks.

1995年，Stuart Kauffman提出生命最初是以自催化化学网络的形式出现的。

The best-known reaction, the BZ reaction, can be created with a mixture of potassium bromate <chem>(KBrO3)</chem>, malonic acid <chem>(CH2(COOH)2)</chem>, and manganese sulfate <chem>(MnSO4)</chem> prepared in a heated solution with sulfuric acid <chem>(H2SO4)</chem> as solvent.<ref>{{Cite web|url=http://online.redwoods.cc.ca.us/instruct/darnold/deproj/Sp98/Gabe/|title=The Belousov-Zhabotinsky Reaction|last=Peterson|first=Gabriel|date=|website=|accessdate=|archiveurl=https://web.archive.org/web/20121231011212/http://online.redwoods.cc.ca.us/instruct/darnold/deproj/Sp98/Gabe/|archivedate=December 31, 2012}}</ref>

British ethologist Richard Dawkins wrote about autocatalysis as a potential explanation for abiogenesis in his 2004 book The Ancestor's Tale. He cites experiments performed by Julius Rebek and his colleagues at the Scripps Research Institute in California in which they combined amino adenosine and pentafluorophenyl ester with the autocatalyst amino adenosine triacid ester (AATE). One system from the experiment contained variants of AATE which catalyzed the synthesis of themselves. This experiment demonstrated the possibility that autocatalysts could exhibit competition within a population of entities with heredity, which could be interpreted as a rudimentary form of natural selection, and that certain environmental changes (such as irradiation) could alter the chemical structure of some of these self-replicating molecules (an analog for mutation) in such ways that could either boost or interfere with its ability to react, thus boosting or interfering with its ability to replicate and spread in the population.

英国动物行为学家 Richard Dawkins在他2004年出版的《祖先的故事》一书中提到了自我催化作为自然发生的潜在解释。他引用了 Julius Rebek 和他的同事们在加利福尼亚斯克里普斯研究所进行的实验，他们将氨基腺苷和五氟苯酯与氨基腺苷三酸酯(AATE)结合在一起。实验中的一个系统包含了催化自身合成的 AATE 的变体。这项实验证明了这样一种可能性，即自动催化剂可以在具有遗传性的实体群体中展现竞争，这可以被解释为一种基本的自然选择形式，而且某些环境变化(如辐照)可以改变某些自我复制分子(变异的类似物)的化学结构，这种方式可以增强或干扰其反应能力，从而增强或干扰其复制和在群体中传播的能力。

== Optics example光学实例 ==

Autocatalysis plays a major role in the processes of life. Two researchers who have emphasized its role in the origins of life are Robert Ulanowicz and Stuart Kauffman.

自动催化在生命过程中起着重要的作用。强调其在生命起源中的作用的两位研究人员是Robert Ulanowicz和Stuart Kauffman。

Another autocatalytic system is one driven by light coupled to photo-polymerization reactions. In a process termed optical autocatalysis, positive feedback is created between light intensity and photo-polymerization rate, via polymerization-induced increases in the refractive index. Light's preference to occupy regions of higher refractive index results in leakage of light into regions of higher molecular weight, thereby amplifying the photo-chemical reaction. The positive feedback may be expressed as:<ref name=":0">{{Cite journal|last=Biria|first=Saeid|last2=Malley|first2=Phillip P. A.|last3=Kahan|first3=Tara F.|last4=Hosein|first4=Ian D.|date=2016-11-15|title=Optical Autocatalysis Establishes Novel Spatial Dynamics in Phase Separation of Polymer Blends during Photocuring|journal=ACS Macro Letters|volume=5|issue=11|pages=1237–1241|doi=10.1021/acsmacrolett.6b00659}}</ref>

Autocatalysis occurs in the initial transcripts of rRNA. The introns are capable of excising themselves by the process of two nucleophilic transesterification reactions. The RNA able to do this is sometimes referred to as a ribozyme. Additionally, the citric acid cycle is an autocatalytic cycle run in reverse.

自我催化发生在RNA的最初转录本中。这些内含子能够通过两个亲核酯交换反应反应自我激活。能够做到这一点的 RNA 有时被称为核酶。此外，三羧酸循环是一种反向运行的自动催化循环。

:<math>\text{polymerization rate} \to \text{molecular weight}/\text{refractive index} \to \text{intensity}</math>

Ultimately, biological metabolism itself can be seen as a vast autocatalytic set, in that all of the molecular constituents of a biological cell are produced by reactions involving this same set of molecules.

最终，生物的新陈代谢本身可以被看作是一个巨大的自我催化装置，因为一个生物细胞的所有分子成分都是由包含同一组分子的反应产生的。

Noting that photo-polymerization rate is proportional to intensity<ref>{{Cite journal|last=Decker|first=Christian|date=1998-02-01|title=The use of UV irradiation in polymerization|url=|journal=Polymer International|language=en|volume=45|issue=2|pages=133–141 |doi=10.1002/(SICI)1097-0126(199802)45:2<133::AID-PI969>3.0.CO;2-F}}</ref> and that refractive index is proportional to molecular weight,<ref>{{Cite journal|last=Askadskii|first=A. A.|year=1990|title=Influence of crosslinking density on the properties of polymer networks|journal=Polymer Science U.S.S.R.|volume=32|issue=10|pages=2061–2069|doi=10.1016/0032-3950(90)90361-9}}</ref> the positive feedback between intensity and photo-polymerization establishes the auto-catalytic behavior. Optical auto-catalysis has been shown to result on spontaneous [[pattern formation]] in photopolymers.<ref>{{Cite journal|last=Burgess|first=Ian B.|last2=Shimmell|first2=Whitney E.|last3=Saravanamuttu|first3=Kalaichelvi|date=2007-04-01|title=Spontaneous Pattern Formation Due to Modulation Instability of Incoherent White Light in a Photopolymerizable Medium|journal=Journal of the American Chemical Society|volume=129|issue=15|pages=4738–4746|doi=10.1021/ja068967b|pmid=17378567|issn=0002-7863}}</ref><ref>{{Cite journal|last=Basker|first=Dinesh K.|last2=Brook|first2=Michael A.|last3=Saravanamuttu|first3=Kalaichelvi|title=Spontaneous Emergence of Nonlinear Light Waves and Self-Inscribed Waveguide Microstructure during the Cationic Polymerization of Epoxides|journal=The Journal of Physical Chemistry C|language=en|volume=119|issue=35|pages=20606–20617|doi=10.1021/acs.jpcc.5b07117|year=2015}}</ref><ref>{{Cite journal|last=Biria|first=Saeid|last2=Malley|first2=Philip P. A.|last3=Kahan|first3=Tara F.|last4=Hosein|first4=Ian D.|date=2016-03-03|title=Tunable Nonlinear Optical Pattern Formation and Microstructure in Cross-Linking Acrylate Systems during Free-Radical Polymerization|journal=The Journal of Physical Chemistry C|volume=120|issue=8|pages=4517–4528|doi=10.1021/acs.jpcc.5b11377|issn=1932-7447}}</ref> Hosein and co-workers discovered that optical autocatalysis can also occur in photoreactive polymer blends, and that the process can induce binary phase morphologies with the same pattern as the light profile.<ref name=":0" /> The light undergoes optical [[Modulational instability|modulation instability]], spontaneous dividing into a multitude of optical filaments, and the polymer system thereby forms filaments within the blend structure.<ref name=":0" /> The result is a new system that couples optical autocatalytic behavior to [[spinodal decomposition]].
注意到光聚合速率与强度成正比，折射率与分子量成正比，强度和光聚合之间的正反馈建立了自催化行为。光自催化已经被证明可以导致光聚合物中自发图案的形成。Hosein和他的同事发现，光自催化也可以发生在光活性聚合物混合物中，并且该过程可以诱导具有与光轮廓相同图案的二元相形态。光经历了光调制不稳定性，自发地分裂成许多光学细丝，因此，聚合物系统在共混结构中形成细丝。结果是一个将光学自催化行为与旋节分解相耦合的新系统。

==Biological example生物实例==

It is known that an important metabolic cycle, [[glycolysis]], displays temporal order.<ref>{{cite book | author=G. Nicolis and [[Ilya Prigogine]] | title=Self-Organization in Nonequilibrium Systems | location= New York | publisher=John Wiley and Sons| year=1977 | isbn=978-0-471-02401-9}}

</ref> Glycolysis consists of the degradation of one molecule of glucose and the overall production of two molecules of [[Adenosine triphosphate|ATP]]. The process is therefore of great importance to the energetics of living cells. The global glycolysis reaction involves [[glucose]], [[Adenosine diphosphate|ADP]], [[Nicotinamide adenine dinucleotide|NAD]], [[Pyruvic acid|pyruvate]], [[Adenosine triphosphate|ATP]], and NADH.
糖酵解包括一个葡萄糖分子的降解和两个分子[[三磷酸腺苷| ATP]]的合成。因此，这个过程对活细胞的能量学非常重要。全局糖酵解反应涉及[[葡萄糖]]、[[二磷酸腺苷| ADP]]、[[烟酰胺腺嘌呤二核苷酸| NAD]]

:<chem>glucose{} + 2ADP{} + 2P_\mathit{i}{} + 2NAD -> 2(pyruvate){} + 2ATP{} + 2NADH</chem>.

The details of the process are quite involved, however, a section of the process is autocatalyzed by [[phosphofructokinase]] (PFK). This portion of the process is responsible for oscillations in the pathway that lead to the process oscillating between an active and an inactive form. Thus, the autocatalytic reaction can modulate the process.

过程的细节是相当复杂的，然而，过程的一部分是由[[磷酸果糖激酶]]（PFK）自动催化的。这个过程的这一部分负责路径中的振荡，导致过程在一个活跃的和一个不活跃的形式之间振荡。因此，自催化反应可以调节这一过程。

==Shape tailoring of thin layers薄层剪裁==

It is possible to use the results from an autocatalytic reaction coupled with [[reaction–diffusion system]] theory to tailor the design of a thin layer. The autocatalytic process allows controlling the nonlinear behavior of the oxidation [[Front (physics)|front]], which is used to establish the initial geometry needed to generate the arbitrary final geometry.<ref>{{cite journal |last1=Alfaro-Bittner |first1=K. |last2=Rojas |first2=R.G. |last3=Lafleur |first3=G. |last4=Calvez |first4=S. |last5=Almuneau |first5=G. |last6=Clerc |first6=M.G. |last7=Barbay |first7=S. |title=Modeling the Lateral Wet Oxidation of into Arbitrary Mesa Geometries |journal=Physical Review Applied|date=22 April 2019|volume=11 |issue=4|page=044067|doi=10.1103/PhysRevApplied.11.044067|url=https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.11.044067}}</ref> It has been successfully done in the wet oxidation of <math>Al_xGa_{1-x}As</math> to obtain arbitrary shaped layers of <math>AlO_x</math>.
利用自催化反应与[[反应-扩散系统]]理论相结合的结果，可以定制薄层的设计。自动催化过程允许控制氧化的非线性行为，用于建立生成任意最终几何体所需的初始几何体

==Phase transitions相变==

The initial amounts of reactants determine the distance from a chemical equilibrium of the system. The greater the initial concentrations the further the system is from equilibrium. As the initial concentration increases, an abrupt change in [[entropy|order]] occurs. This abrupt change is known as [[phase transition]]. At the phase transition, fluctuations in macroscopic quantities, such as chemical concentrations, increase as the system oscillates between the more ordered state (lower entropy, such as ice) and the more disordered state (higher entropy, such as liquid water). Also, at the phase transition, macroscopic equations, such as the rate equations, fail. Rate equations can be derived from microscopic considerations. The derivations typically rely on a [[mean field theory]] approximation to microscopic dynamical equations. Mean field theory breaks down in the presence of large fluctuations (see [[Mean field theory]] article for a discussion). Therefore, since large fluctuations occur in the neighborhood of a phase transition, macroscopic equations, such as rate equations, fail. As the initial concentration increases further, the system settles into an ordered state in which fluctuations are again small. (see Prigogine reference)

反应物的初始量决定了与体系化学平衡的距离。初始浓度越大，系统离平衡越远。随着初始浓度的增加，[[熵|阶]]发生突变。这种突变被称为[[相变]]。在相变阶段，宏观量的波动，如化学浓度，随着系统在更有序的状态（低熵，如冰）和更无序的状态（更高的熵，如液态水）之间振荡而增加。同样，在相变过程中，宏观方程，如速率方程，会失效。速率方程可以从微观角度推导出来。推导通常依赖于对微观动力学方程的[[平均场理论]]近似。平均场理论在大波动的情况下会崩溃（见[[平均场理论]]文章进行讨论）。因此，由于大的波动发生在相变附近，宏观方程，如速率方程，失败了。随着初始浓度的进一步增加，系统进入有序状态，在这种状态下波动又很小。（见Prigogine参考文献）

==Asymmetric autocatalysis不对称自催化 ==

Asymmetric autocatalysis occurs when the reaction product is [[chiral]] and thus acts as a chiral catalyst for its own production. Reactions of this type, such as the [[Soai reaction]], have the property that they can amplify a very small [[enantiomeric excess]] into a large one. This has been proposed as an important step in the origin of biological [[homochirality]].<ref name="Soai2001">{{cite journal|vauthors=Soai K, Sato I, Shibata T | title=Asymmetric autocatalysis and the origin of chiral homogeneity in organic compounds. | journal=The Chemical Record | year= 2001 | volume= 1 | issue= 4 | pages= 321–32 | pmid=11893072 | doi= 10.1002/tcr.1017| pmc= }}</ref>
非对称自催化发生在反应产物为[[手性]]时，因此作为手性催化剂进行自身生产。这种类型的反应，如[[Soai反应]]，具有将很小的[[对映体过量]]放大为大反应的性质。在这一点上，手性被认为是生物起源的一个重要步骤

== Role in origin of life生命起源中的角色 ==

{{main|Abiogenesis}}

In 1995 [[Stuart Kauffman]] proposed that life initially arose as autocatalytic chemical networks.<ref>{{cite book|author=Stuart Kauffman|title=At Home in the Universe: The Search for the Laws of Self-Organization and Complexity|isbn=978-0-19-509599-9|publisher=Oxford University Press|year=1995|url-access=registration|url=https://archive.org/details/athomeinuniverse00kauf_0}}</ref>
1995年[[Stuart Kauffman]]提出生命最初是以自催化化学网络的形式出现的

Category:Catalysis

类别: 催化

<noinclude>

This page was moved from [[wikipedia:en:Autocatalysis]]. Its edit history can be viewed at [[自催化/edithistory]]</noinclude>

[[Category:待整理页面]]

自催化

2020-12-25T09:11:51Z

Yetmings：

此词条暂由Henry 翻译。

{{more citations needed|date=September 2010}}

A single [[chemical reaction]] is said to be '''autocatalytic''' if one of the reaction products is also a [[catalyst]] for the same or a coupled reaction.<ref name=Steinfeld>Steinfeld J.I., Francisco J.S. and Hase W.L. ''Chemical Kinetics and Dynamics'' (2nd ed., Prentice-Hall 1999) p.151-2 {{ISBN|0-13-737123-3}}</ref> Such a reaction is called an '''autocatalytic reaction'''.

A single chemical reaction is said to be autocatalytic if one of the reaction products is also a catalyst for the same or a coupled reaction. Such a reaction is called an autocatalytic reaction.

一个单一的化学反应，如果其中一个反应产物也是同一反应或耦合反应的催化剂，则称为具有自催化性质。这种反应称为 自催化反应autocatalytic reaction。

A ''set'' of chemical reactions can be said to be "collectively autocatalytic" if a number of those reactions produce, as reaction products, catalysts for enough of the other reactions that the entire set of chemical reactions is self-sustaining given an input of energy and food molecules (see [[autocatalytic set]]).

A set of chemical reactions can be said to be "collectively autocatalytic" if a number of those reactions produce, as reaction products, catalysts for enough of the other reactions that the entire set of chemical reactions is self-sustaining given an input of energy and food molecules (see autocatalytic set).

如果一系列化学反应作为反应产物产生足够多的其他反应的催化剂，使整套化学反应在能量和食物分子输入的情况下能够自我维持，则可以说这些化学反应是”集体自我催化”的。

==Chemical reactions化学反应==

{{main|Chemical reaction|Chemical kinetics}}

A chemical reaction of two reactants and two products can be written as

A chemical reaction of two reactants and two products can be written as

两种反应物和两种产物的化学反应可以写成

:<math> \alpha A + \beta B \rightleftharpoons \sigma S + \tau T</math>

<math> \alpha A + \beta B \rightleftharpoons \sigma S + \tau T</math>

where the Greek letters are [[stoichiometric coefficients]] and the capital Latin letters represent chemical species. The chemical reaction proceeds in both the forward and reverse direction. This equation is easily generalized to any number of reactants, products, and reactions.

where the Greek letters are stoichiometric coefficients and the capital Latin letters represent chemical species. The chemical reaction proceeds in both the forward and reverse direction. This equation is easily generalized to any number of reactants, products, and reactions.

其中希腊字母是化学计量系数，大写拉丁字母代表化学物种。化学反应在正向和反向两个方向进行。这个方程可以很容易地推广到任意数量的反应物、产物和反应。

===Chemical equilibrium化学平衡===

In [[chemical equilibrium]] the forward and reverse [[reaction rate]]s are such that each chemical species is being created at the same rate it is being destroyed. In other words, the rate of the forward reaction is equal to the rate of the reverse reaction.

In chemical equilibrium the forward and reverse reaction rates are such that each chemical species is being created at the same rate it is being destroyed. In other words, the rate of the forward reaction is equal to the rate of the reverse reaction.

在化学平衡状态，正向和反向的反应速率是这样的情况：每一种化学物质都以同样的速率生成和消失。换句话说，正向反应的速率等于反向反应的速率。

:<math> k_+ [ A ]^\alpha [B ]^\beta = k_{-} [S ]^\sigma[T ]^\tau \,</math>

<math> k_+ [ A ]^\alpha [B ]^\beta = k_{-} [S ]^\sigma[T ]^\tau \,</math>

K _ + [ a ] ^ alpha [ b ] ^ beta = k _ {-}[ s ] ^ sigma [ t ] ^ tau，</math >

Here, the brackets indicate the concentration of the chemical species, in [[mole (unit)|moles]] per liter, and k+ and k− are [[rate constant]]s.

Here, the brackets indicate the concentration of the chemical species, in moles per liter, and k+ and k− are rate constants.

这里，括号表示化学物质的浓度，以摩尔/升为单位，k+和 k-是速率常数。

===Far from equilibrium远离平衡态===

Far from equilibrium, the forward and reverse reaction rates no longer balance and the concentration of reactants and products is no longer constant. For every forward reaction <math>\alpha </math> molecules of A are destroyed. For every reverse reaction <math>\alpha </math> molecules of A are created. In the case of an [[elementary reaction]] step the [[reaction order]] in each direction equals the molecularity, so that the rate of change in the number of moles of A is then

Far from equilibrium, the forward and reverse reaction rates no longer balance and the concentration of reactants and products is no longer constant. For every forward reaction <math>\alpha </math> molecules of A are destroyed. For every reverse reaction <math>\alpha </math> molecules of A are created. In the case of an elementary reaction step the reaction order in each direction equals the molecularity, so that the rate of change in the number of moles of A is then

在远离平衡态时，正向和反向反应速率不再是平衡的，反应物和产物的浓度不再是恒定的。对于每一个前向反应，a 的分子会消失。对于每一个逆反应，a 的分子都会被产生出来。在基本反应步骤中，每个方向的反应级数等于“反应分子数”（molecularity），因此 a 的摩尔数的变化率就是

:<math>{d \over dt}[ A ] =-\alpha k_+ [ A ]^\alpha [B ]^\beta +\alpha k_{-} [S ]^\sigma[T ]^\tau \,</math>

<math>{d \over dt}[ A ] =-\alpha k_+ [ A ]^\alpha [B ]^\beta +\alpha k_{-} [S ]^\sigma[T ]^\tau \,</math>

[ a ] =-alpha k _ + [ a ] ^ alpha [ b ] ^ beta + alpha k _ {-}[ s ] ^ sigma [ t ] ^ tau，</math >

:<math>{d \over dt}[ B ] =-\beta k_+ [ A ]^\alpha [B ]^\beta +\beta k_{-} [S ]^\sigma[T ]^\tau \,</math>

<math>{d \over dt}[ B ] =-\beta k_+ [ A ]^\alpha [B ]^\beta +\beta k_{-} [S ]^\sigma[T ]^\tau \,</math>

[ b ] =-beta k _ + [ a ] ^ alpha [ b ] ^ beta + beta k _ {-}[ s ] ^ sigma [ t ] ^ tau，</math >

:<math>{d \over dt}[ S ] =\sigma k_+ [ A ]^\alpha [B ]^\beta -\sigma k_{-} [S ]^\sigma[T ]^\tau \,</math>

<math>{d \over dt}[ S ] =\sigma k_+ [ A ]^\alpha [B ]^\beta -\sigma k_{-} [S ]^\sigma[T ]^\tau \,</math>

[ s ] = sigma k _ + [ a ] ^ alpha [ b ] ^ beta-sigma k _ {-}[ s ] ^ sigma [ t ] ^ tau，</math >

:<math>{d \over dt}[ T ] =\tau k_+ [ A ]^\alpha [B ]^\beta -\tau k_{-} [S ]^\sigma[T ]^\tau \,</math>

<math>{d \over dt}[ T ] =\tau k_+ [ A ]^\alpha [B ]^\beta -\tau k_{-} [S ]^\sigma[T ]^\tau \,</math>

[ t ] = tau k _ + [ a ] ^ alpha [ b ] ^ beta-tau k _ {-}[ s ] ^ sigma [ t ] ^ tau，</math >

This system of equations has a single stable [[Fixed point (mathematics)|fixed point]] when the forward rates and the reverse rates are equal (when <math>{d \over dt}=0</math> for every species). This means that the system evolves to the equilibrium state, and this is the only state to which it evolves.<ref>{{cite journal |last1=Ross |first1=John |last2=Garcia-Colin |first2=Leopoldo S. |title=Thermodynamics of chemical systems far from equilibrium |journal=The Journal of Physical Chemistry |date=March 1989 |volume=93 |issue=5 |pages=2091–2092 |doi=10.1021/j100342a075}}</ref>

This system of equations has a single stable fixed point when the forward rates and the reverse rates are equal (when <math>{d \over dt}=0</math> for every species). This means that the system evolves to the equilibrium state, and this is the only state to which it evolves.

这个系统的方程组有一个单一的稳定不动点解，这个解的情况就是每个物种的正向速率和反向速率相等。这意味着这个系统是往平衡状态演化，而且这个平衡状态这是系统演化到的唯一状态。

===Autocatalytic reactions自催化反应===

[[Image:Sigmoid curve for an autocatalytical reaction.jpg|256px|right|thumb|Sigmoid variation of product concentration in autocatalytic reactions]]

Sigmoid variation of product concentration in autocatalytic reactions

自催化反应中产物浓度的 s 形变化

Autocatalytic reactions are those in which at least one of the products is a reactant. Perhaps the simplest autocatalytic reaction can be written<ref name=Steinfeld/>

Autocatalytic reactions are those in which at least one of the products is a reactant. Perhaps the simplest autocatalytic reaction can be written

自催化反应是那些其中至少一个产物是反应物的反应。最简单的自催化反应可以是这样的形式

:<math> A + B \rightleftharpoons 2B</math>

<math>[A]=\frac{[A]_0+[B]_0}{1+\frac{[B]_0}{[A]_0}e^{([A]_0+[B]_0)kt}}</math>

< math > [ a ] = frac {[ a ] _ 0 + [ b ] _ 0}{1 + frac {[ b ] _ 0}{[ a ] _ 0} e ^ {(([ a ] _ 0 + [ b ] _ 0) kt }} </math >

and

及

with the rate equations (for an elementary reaction)

<math>[B]=\frac{[A]_0+[B]_0}{1+\frac{[A]_0}{[B]_0}e^{-([A]_0+[B]_0)kt}}</math>.

< math > [ b ] = frac {[ a ] _ 0 + [ b ] _ 0}{1 + frac {[ a ] _ 0}{[ b ] _ 0} e ^ {-([ a ] _ 0 + [ b ] _ 0) kt }} </math > .

:<math>{d \over dt}[ A ] =- k_+ [ A ] [B ] + k_{-} [B ]^2 \,</math>

The graph for these equations is a sigmoid curve (specifically a logistic function), which is typical for autocatalytic reactions: these chemical reactions proceed slowly at the start (the induction period) because there is little catalyst present, the rate of reaction increases progressively as the reaction proceeds as the amount of catalyst increases and then it again slows down as the reactant concentration decreases. If the concentration of a reactant or product in an experiment follows a sigmoid curve, the reaction may be autocatalytic.

这些方程的曲线图是一条s形曲线（特别是logistic函数），这是自催化反应的典型特征：这些化学反应在开始时（诱导期）进行得很慢，因为几乎没有催化剂存在，随着催化剂用量的增加，反应速度逐渐增加，然后随着反应物浓度的降低，反应速度再次减慢。如果一个实验中反应物或产物的浓度服从s形曲线，则该反应可能是自催化的。

:<math>{d \over dt}[ B ] = + k_+ [ A ] [B ] -k_{-} [B ]^2 \,</math>.

These kinetic equations apply for example to the acid-catalyzed hydrolysis of some esters to carboxylic acids and alcohols. In the hurricane example, hurricanes are formed from unequal heating within the atmosphere. The Earth's atmosphere is then far from thermal equilibrium. The order of the Earth's atmosphere increases, but at the expense of the order of the sun. The sun is becoming more disorderly as it ages and throws off light and material to the rest of the universe. The total disorder of the sun and the earth increases despite the fact that orderly hurricanes are generated on earth.

这些动力学方程适用于一些酯的酸催化水解为羧酸和醇。在飓风的例子中，飓风是由大气中不均匀的加热形成的。地球的大气层离热平衡还很远。地球大气的秩序增加了，但以太阳的秩序为代价。随着年龄的增长，太阳正变得越来越无序，并向宇宙的其他部分发射光和物质。尽管有秩序的飓风随时都会发生，但太阳和地球的整体混乱程度却在增加。

This reaction is one in which a molecule of species A interacts with a molecule of species B. The A molecule is converted into a B molecule. The final product consists of the original B molecule plus the B molecule created in the reaction.

这个反应是物种A的分子与物种B的分子相互作用，A分子转化为B分子。最终产物由原始的B分子加上反应中产生的B分子组成。

A similar example exists for living chemical systems. The sun provides energy to green plants. The green plants are food for other living chemical systems. The energy absorbed by plants and converted into chemical energy generates a system on earth that is orderly and far from chemical equilibrium. Here, the difference from chemical equilibrium is determined by an excess of reactants over the equilibrium amount. Once again, order on earth is generated at the expense of entropy increase of the sun. The total entropy of the earth and the rest of the universe increases, consistent with the Second Law.

类似的例子也存在于活的化学系统中。太阳为绿色植物提供能量。绿色植物是其他生命化学系统的食物。植物吸收并转化为化学能的能量在地球上形成了一个有序的系统，这个系统远离化学平衡。在这里，反应物超过平衡量决定了化学平衡的差异。再一次，地球上的秩序是以太阳的熵增为代价而产生的。地球和宇宙其余部分的总熵增加，符合第二定律。

The key feature of these rate equations is that they are [[nonlinear]]; the second term on the right varies as the square of the concentration of B. This feature can lead to multiple fixed points of the system, much like a [[quadratic equation]] can have multiple roots. Multiple fixed points allow for multiple states of the system. A system existing in multiple [[macroscopic]] states is more orderly (has lower entropy) than a system in a single state.
这些速率方程的关键特征是它们是[[非线性]；右边的第二项随B浓度的平方而变化。这一特性可导致系统的多个不动点，就像[[二次方程]]可以有多个根一样。多个固定点允许系统的多种状态。存在于多个[[宏观]]状态的系统比处于单一状态的系统更有序（熵更低）。

Some autocatalytic reactions also generate order in a system at the expense of its surroundings. For example, (clock reactions) have intermediates whose concentrations oscillate in time, corresponding to temporal order. Other reactions generate spatial separation of chemical species corresponding to spatial order. More complex reactions are involved in metabolic pathways and metabolic networks in biological systems.

一些自催化反应也以牺牲周围环境为代价，在系统中产生有序。例如，(时钟反应)有其浓度在时间上振荡的中间体，对应于时间顺序。其他反应产生空间分离的化学物质对应的空间秩序。更复杂的反应涉及到生物系统中的代谢途径和代谢网络。

The concentrations of A and B vary in time according to<ref name=Steinfeld/><ref name=Moore>Moore J.W. and [[Ralph Pearson|Pearson R.G.]] ''Kinetics and Mechanism'' (John Wiley 1981) p.26 {{ISBN|0-471-03558-0}}</ref>

:<math>[A]=\frac{[A]_0+[B]_0}{1+\frac{[B]_0}{[A]_0}e^{([A]_0+[B]_0)kt}}</math>

The transition to order as the distance from equilibrium increases is not usually continuous. Order typically appears abruptly. The threshold between the disorder of chemical equilibrium and order is known as a phase transition. The conditions for a phase transition can be determined with the mathematical machinery of non-equilibrium thermodynamics.

随着离平衡距离的增加，向有序的过渡通常是不连续的。秩序通常会突然出现。化学平衡和有序之间的无序阈值被称为相变。相变的条件可以用非平衡态热力学的数学方法来确定。

and

:<math>[B]=\frac{[A]_0+[B]_0}{1+\frac{[A]_0}{[B]_0}e^{-([A]_0+[B]_0)kt}}</math>.

The graph for these equations is a [[sigmoid function|sigmoid curve]] (specifically a [[logistic function]]), which is typical for autocatalytic reactions: these chemical reactions proceed slowly at the start (the [[induction period]]) because there is little catalyst present, the rate of reaction increases progressively as the reaction proceeds as the amount of catalyst increases and then it again slows down as the reactant concentration decreases. If the concentration of a reactant or product in an experiment follows a sigmoid curve, the reaction may be autocatalytic.
这些方程的图形是一个[[西格莫函数| S形曲线]]（特别是[[逻辑函数]]），这是自催化反应的典型特征：这些化学反应在开始时（诱导期]]）进行得很慢，因为催化剂很少，随着催化剂用量的增加，反应速度逐渐增加，然后随着反应物浓度的降低，反应速度再次减慢。如果一个实验中反应物或产物的浓度服从sigmoid曲线，则该反应可能是自催化的。
A chemical reaction cannot oscillate about a position of final equilibrium because the second law of thermodynamics requires that a thermodynamic system approach equilibrium and not recede from it. For a closed system at constant temperature and pressure, the Gibbs free energy must decrease continuously and not oscillate. However it is possible that the concentrations of some reaction intermediates oscillate, and also that the rate of formation of products oscillates.

一个化学反应不能在一个最终平衡位置上振荡，因为热力学第二定律需要一个接近平衡的热力学系统，而不能退出平衡位置。对于一个温度和压力恒定的封闭系统， 吉布斯自由能Gibbs free energy必须不断减小而不振荡。然而，一些反应中间体的浓度可能会振荡，产物的生成速率也可能振荡。

These kinetic equations apply for example to the acid-catalyzed hydrolysis of some [[ester]]s to [[carboxylic acid]]s and [[alcohol]]s.<ref name=Moore/> There must be at least some acid present initially to start the catalyzed mechanism; if not the reaction must start by an alternate uncatalyzed path which is usually slower. The above equations for the catalyzed mechanism would imply that the concentration of acid product remains zero forever.<ref name=Moore/>
例如，这些动力学方程适用于某些[[酯]]到[[羧酸]]和[[醇]]的酸催化水解。最初必须至少存在一些酸来启动催化机制；否则，反应必须通过通常较慢的替代非催化路径开始。上述催化机理的方程式意味着酸产物的浓度永远为零。

The Lotka–Volterra equation is [[isomorphic with the predator–prey model and the two-reaction autocatalytic model. In this example baboons and cheetahs are equivalent to two different chemical species X and Y in autocatalytic reactions.]]

方程[同构于捕食-食饵模型和双反应自催化模型。在这个例子中，狒狒和猎豹在自动催化反应中相当于两种不同的化学物种 x 和 y

==Creation of order秩序创立==

Consider a coupled set of two autocatalytic reactions in which the concentration of one of the reactants A is much larger than its equilibrium value. In this case, the forward reaction rate is so much larger than the reverse rates that we can neglect the reverse rates.

考虑一组耦合的两个自催化反应，其中一个反应物 a 的浓度远远大于其平衡值。在这种情况下，正向反应速率远远大于反向反应速率，因此我们可以忽略反向反应速率。

===Background背景===

<math> A + X \rightarrow 2X</math>

A + x 右行2X

The [[second law of thermodynamics]] states that the disorder ([[entropy]]) of a physical or chemical system and its surroundings (a [[closed system]]) must increase with time. Systems left to themselves become increasingly [[random]], and orderly energy of a system like uniform motion degrades eventually to the random motion of particles in a [[heat bath]].
[[热力学第二定律]指出，物理或化学系统及其周围环境（封闭系统）的无序度（[[熵]]）必须随时间而增加。留给自己的系统变得越来越[[随机]]，系统的有序能量（如均匀运动）最终退化为粒子在[[热浴]中的随机运动
<math> X + Y \rightarrow 2Y</math>

(数学) x + y 右行2Y

There are, however, many instances in which physical systems spontaneously become [[emergence|emergent]] or orderly. For example, despite the destruction they cause, [[hurricane]]s have a very orderly [[vortex]] motion when compared to the random motion of the air molecules in a closed room. Even more spectacular is the order created by chemical systems; the most dramatic being the order associated with life.
然而，在许多情况下，物理系统自发地变得新生或有序。例如，尽管飓风造成了破坏，但与封闭房间中空气分子的随机运动相比，[[飓风]]的运动非常有序。更引人注目的是化学系统创造的秩序；最引人注目的是与生命相关的秩序。
<math> Y \rightarrow E</math>

[数学，数学]

This is consistent with the Second Law, which requires that the total disorder of a system ''and its surroundings'' must increase with time. Order can be created in a system by an even greater decrease in order of the system's surroundings.<ref>{{cite book | author=Ilya Prigogine | title=From Being to Becoming: Time and Complexity in the Physical Sciences | location=San Francisco | publisher=W. H. Freeman | year=1980 | isbn=978-0-7167-1107-0 | author-link=Ilya Prigogine | url-access=registration | url=https://archive.org/details/frombeingtobecom00ipri }}
这与第二定律是一致的，第二定律要求系统“及其周围环境”的整体无序程度必须随时间而增加。在一个系统中，秩序可以通过系统周围环境的更大程度的降低而产生
with the rate equations

用速率方程式

</ref> In the hurricane example, hurricanes are formed from unequal heating within the atmosphere. The Earth's atmosphere is then far from [[thermal equilibrium]]. The order of the Earth's atmosphere increases, but at the expense of the order of the sun. The sun is becoming more disorderly as it ages and throws off light and material to the rest of the universe. The total disorder of the sun and the earth increases despite the fact that orderly hurricanes are generated on earth.

在飓风的例子中，飓风是由大气中不均匀的加热形成的。地球的大气层离[[热平衡]]很远。地球大气的秩序增加了，但以太阳的秩序为代价。随着年龄的增长，太阳正变得越来越无序，并向宇宙的其他部分发射光和物质。尽管地球上产生了有序的飓风，但太阳和地球的总体混乱程度却在增加。

<math>{d \over dt}[ X ] = k_1 [ A ] [X ] - k_{2} [X ][Y ] \,</math>

< math > { d over dt }[ x ] = k_1[ a ][ x ]-k_2}[ x ][ y ] ，</math >

A similar example exists for living chemical systems. The sun provides energy to green plants. The green plants are food for other living chemical systems. The energy absorbed by plants and converted into chemical energy generates a system on earth that is orderly and far from [[chemical equilibrium]]. Here, the difference from chemical equilibrium is determined by an excess of reactants over the equilibrium amount. Once again, order on earth is generated at the expense of entropy increase of the sun. The total entropy of the earth and the rest of the universe increases, consistent with the Second Law.

生命化学系统也有类似的例子。太阳为绿色植物提供能量。绿色植物是其他生物化学系统的食物。被植物吸收并转化为化学能的能量在地球上产生了一个有序的、远离[化学平衡]的系统。在这里，与化学平衡的差异是由反应物超过平衡量所决定的。地球上的秩序再一次以太阳的熵增加为代价。地球和宇宙其他部分的总熵增加，符合第二定律

<math>{d \over dt}[ Y ] = k_2 [ X ] [Y ] - k_{3} [Y ] \,</math>.

[ y ] = k _ 2[ x ][ y ]-k _ {3}[ y ] ，[/math ].

Some autocatalytic reactions also generate order in a system at the expense of its surroundings. For example, ([[clock reactions]]) have [[reaction intermediate|intermediates]] whose concentrations oscillate in time, corresponding to temporal order. Other reactions generate spatial separation of [[chemical species]] corresponding to spatial order. More complex reactions are involved in [[metabolic pathway]]s and [[metabolic network]]s in [[biological systems]].
一些自催化反应也以牺牲周围环境为代价在系统中产生秩序。例如，（[[时钟反应]]）有[[反应中间体|中间体]]，其浓度随时间振荡，与时间顺序相对应。其他反应产生空间分离[[化学物种]]对应的空间顺序。在[[生物系统]]中的[[代谢途径]]s和[[代谢网络]]涉及更复杂的反应

Here, we have neglected the depletion of the reactant A, since its concentration is so large. The rate constants for the three reactions are <math>k_1</math>, <math>k_2</math>, and <math>k_3</math>, respectively.

在这里，我们忽略了反应物 a 的耗尽，因为它的浓度很大。这三个反应的速率常数分别是k1,k2,k3 。

The transition to order as the distance from equilibrium increases is not usually continuous. Order typically appears abruptly. The threshold between the disorder of chemical equilibrium and order is known as a [[phase transition]]. The conditions for a phase transition can be determined with the mathematical machinery of [[non-equilibrium thermodynamics]].

随着与平衡的距离增加，向有序的转变通常不是连续的。顺序通常会突然出现。化学平衡与有序之间的界限称为[[相变]]。相变的条件可以用[[非平衡态热力学]的数学机制来确定

This system of rate equations is known as the Lotka–Volterra equation and is most closely associated with population dynamics in predator–prey relationships. This system of equations can yield oscillating concentrations of the reaction intermediates X and Y. The amplitude of the oscillations depends on the concentration of A (which decreases without oscillation). Such oscillations are a form of emergent temporal order that is not present in equilibrium.

这个速率方程组被称为 Lotka-Volterra 方程，在捕食者-食饵关系中与族群动态最密切相关。这个方程组可以产生反应中间体 x 和 y 的振荡浓度。振荡的振幅取决于 a 的浓度(a 的浓度下降而没有振荡)。这种振荡是一种涌现的时间顺序，在平衡中不存在。

===Temporal order时间顺序===

A chemical reaction cannot oscillate about a position of final [[chemical equilibrium|equilibrium]] because the second law of thermodynamics requires that a [[thermodynamic system]] approach equilibrium and not recede from it. For a closed system at constant temperature and pressure, the [[Gibbs free energy]] must decrease continuously and not oscillate. However it is possible that the concentrations of some [[reaction intermediate]]s oscillate, and also that the ''rate'' of formation of products oscillates.<ref>Espenson, J.H. ''Chemical Kinetics and Reaction Mechanisms'' (2nd ed., McGraw-Hill 2002) p.190 {{ISBN|0-07-288362-6}}</ref>
一个化学反应不能围绕最终的[[化学平衡|平衡]]的位置振荡，因为热力学第二定律要求[[热力学系统]]接近平衡，而不是从中退却。对于一个恒温恒压的封闭系统，[[Gibbs自由能]必须连续下降而不振荡。然而，一些[[反应中间体]]的浓度可能会振荡，产物形成的“速率”也会振荡。

====Idealized example: Lotka–Volterra equation理想化例子：Lotka–Volterra 等式====

Another example of a system that demonstrates temporal order is the Brusselator (see Prigogine reference). It is characterized by the reactions

另一个演示时间顺序的系统例子是 Brusselator (见 Prigogine 参考文献)。人们的反应是拥有属性的

[[File:CentralTendencyLV.jpg|thumb|right|350px|The Lotka–Volterra equation is [[isomorphic]] with the predator–prey model and the two-reaction autocatalytic model. In this example baboons and cheetahs are equivalent to two different chemical species X and Y in autocatalytic reactions.]]

Consider a coupled set of two autocatalytic reactions in which the concentration of one of the reactants A is much larger than its equilibrium value. In this case, the forward reaction rate is so much larger than the reverse rates that we can neglect the reverse rates.
考虑一组耦合的两个自催化反应，其中一个反应物a的浓度远远大于其平衡值。在这种情况下，正向反应速率比反向速率大得多，我们可以忽略反向速率。
<math> A \rightarrow X</math>

《数学》 a right tarrow x

:<math> A + X \rightarrow 2X</math>

<math> 2X + Y \rightarrow 3X</math>

2X + y 右行3X

:<math> X + Y \rightarrow 2Y</math>

<math> B + X \rightarrow Y + D</math>

B + x 右边 y + d

:<math> Y \rightarrow E</math>

<math> X \rightarrow E</math>

X 右边的 e

with the rate equations

with the rate equations

用速率方程式

:<math>{d \over dt}[ X ] = k_1 [ A ] [X ] - k_{2} [X ][Y ] \,</math>

<math>{d \over dt}[ X ] = [A ] + [ X ]^2 [Y ] - [B ] [X ] - [X ] \,</math>

< math > { d over dt }[ x ] = [ a ] + [ x ] ^ 2[ y ]-[ b ][ x ]-[ x ] ，</math >

:<math>{d \over dt}[ Y ] = k_2 [ X ] [Y ] - k_{3} [Y ] \,</math>.

<math>{d \over dt}[ Y ] = [B ] [X ] - [ X ]^2 [Y ] \,</math>

[数学]{ d/dt }[ y ] = [ b ][ x ]-[ x ] ^ 2[ y ] ，[/math ]

Here, we have neglected the depletion of the reactant A, since its concentration is so large. The rate constants for the three reactions are <math>k_1</math>, <math>k_2</math>, and <math>k_3</math>, respectively.

where, for convenience, the rate constants have been set to 1.

为了方便起见，速率常数设置为1。

This system of rate equations is known as the [[Lotka–Volterra equation]] and is most closely associated with [[population dynamics]] in predator–prey relationships. This system of equations can yield oscillating concentrations of the reaction intermediates X and Y. The amplitude of the oscillations depends on the concentration of A (which decreases without oscillation). Such oscillations are a form of emergent temporal order that is not present in equilibrium.
这个速率方程组被称为[[Lotka–Volterra equation]]，在捕食者-猎物关系中与[[种群动力学]]联系最为密切。这个方程组可以得到反应中间体X和Y的振荡浓度，振荡的幅度取决于A的浓度（A的浓度减少而不振荡）。这种振荡是一种在平衡状态下不存在的突发时序形式。
The Brusselator in the unstable regime. A=1. B=2.5. X(0)=1. Y(0)=0. The system approaches a [[limit cycle. For B<1+A the system is stable and approaches a fixed point.]]

不稳定政权中的布鲁塞尔振子。 A=1. B=2.5. X(0)=1. Y(0)=0.该系统接近[极限环]。对于 b < 1 + a，系统是稳定的，并且接近一个固定点。]

The Brusselator has a fixed point at

布鲁塞尔振子有一个固定点

====Another idealized example: Brusselator另一个理想化模型：布鲁塞尔振子====

<math>[ X ] = A \,</math>

[数学] = a，[数学]

Another example of a system that demonstrates temporal order is the [[Brusselator]] (see Prigogine reference). It is characterized by the reactions

<math>[ Y ] = {B \over A} \,</math>.

[ math ][ y ] = { b over a } ，[ math ].

:<math> A \rightarrow X</math>

The fixed point becomes unstable when

定点变得不稳定，当

:<math> 2X + Y \rightarrow 3X</math>

<math> B>1+A^2 \,</math>

1 + a ^ 2,

:<math> B + X \rightarrow Y + D</math>

leading to an oscillation of the system. Unlike the Lotka-Volterra equation, the oscillations of the Brusselator do not depend on the amount of reactant present initially. Instead, after sufficient time, the oscillations approach a limit cycle.

导致了系统的振荡。与Lotka-Volterra 方程不同，布鲁塞尔振荡器的振荡并不取决于最初反应物的数量。相反，在足够的时间之后，振荡接近极限环。

:<math> X \rightarrow E</math>

with the rate equations

An idealized example of spatial spontaneous symmetry breaking is the case in which we have two boxes of material separated by a permeable membrane so that material can diffuse between the two boxes. It is assumed that identical Brusselators are in each box with nearly identical initial conditions. (see Prigogine reference)

一个理想化的空间自发对称性破缺的例子是，我们有两个盒子的材料被一个可渗透的薄膜分开，这样材料可以在两个盒子之间扩散。我们假设在每个盒子中都有相同的布鲁塞尔振子，并且具有几乎相同的初始条件。(见 Prigogine 参考文献)

:<math>{d \over dt}[ X ] = [A ] + [ X ]^2 [Y ] - [B ] [X ] - [X ] \,</math>

<math>{d \over dt}[ X_1 ] = [A ] + [ X _1]^2 [Y_1 ] - [B ] [X_1 ] - [X_1 ] + D_x\left( X_2 - X_1 \right)\,</math>

< math > { d over dt }[ x _ 1] = [ a ] + [ x _ 1] ^ 2[ y _ 1]-[ b ][ x _ 1]-[ x _ 1] + d _ x 左(x _ 2-x _ 1右) ，</math >

:<math>{d \over dt}[ Y ] = [B ] [X ] - [ X ]^2 [Y ] \,</math>

<math>{d \over dt}[ Y_1 ] = [B ] [X_1 ] - [ X_1 ]^2 [Y_1 ] + D_y\left( Y_2 - Y_1\right) \,</math>

< math > { d over dt }[ y _ 1] = [ b ][ x _ 1]-[ x _ 1] ^ 2[ y _ 1] + d _ y 左(y _ 2-y _ 1右) ，</math >

where, for convenience, the rate constants have been set to 1.
其中，为了方便起见，速率常数被设置为1。
<math>{d \over dt}[ X_2 ] = [A ] + [ X _2]^2 [Y_2 ] - [B ] [X_2 ] - [X_2 ] + D_x\left( X_1 - X_2 \right)\,</math>

[ x _ 2] = [ a ] + [ x _ 2] ^ 2[ y _ 2]-[ b ][ x _ 2]-[ x _ 2] + d _ x 左(x _ 1-x _ 2右) ，</math >

[[File:080205 Brusselator picture.jpg|thumb|right|350px|The Brusselator in the unstable regime. A=1. B=2.5. X(0)=1. Y(0)=0. The system approaches a [[limit cycle]]. For B<1+A the system is stable and approaches a [[Fixed point (mathematics)|fixed point]].]]

<math>{d \over dt}[ Y_2 ] = [B ] [X_2 ] - [ X_2 ]^2 [Y_2 ] + D_y\left( Y_1 - Y_2\right) \,</math>

[ math ]{ d over dt }[ y _ 2] = [ b ][ x _ 2]-[ x _ 2] ^ 2[ y _ 2] + d _ y 左(y _ 1-y _ 2右) ，</math >

The Brusselator has a fixed point at
布鲁塞尔振子有一个固定点在

Here, the numerical subscripts indicate which box the material is in. There are additional terms proportional to the diffusion coefficient D that account for the exchange of material between boxes.

在这里，数字下标表示材料在哪个盒子里。还有一些与扩散系数 d 成比例的附加项，用于解释盒子之间的物质交换。

:<math>[ X ] = A \,</math>

If the system is initiated with the same conditions in each box, then a small fluctuation will lead to separation of materials between the two boxes. One box will have a predominance of X, and the other will have a predominance of Y.

如果系统启动时每个盒子的条件相同，那么一个小的波动将导致两个盒子之间的物料分离。一个盒子将具有 x 的优势，而另一个盒子将具有 y 的优势。

:<math>[ Y ] = {B \over A} \,</math>.

The fixed point becomes unstable when

固定点变得不稳定当

Real examples of clock reactions are the Belousov–Zhabotinsky reaction (BZ reaction), the Briggs–Rauscher reaction, the Bray–Liebhafsky reaction and the iodine clock reaction. These are oscillatory reactions, and the concentration of products and reactants can be approximated in terms of damped oscillations.

时钟反应的真实例子是 Belousov-Zhabotinsky 反应(BZ 反应) ，Briggs-Rauscher 反应，Bray-Liebhafsky 反应和碘钟反应。这些都是振荡反应，产物和反应物的浓度可以用阻尼振荡来近似。

:<math> B>1+A^2 \,</math>

The best-known reaction, the BZ reaction, can be created with a mixture of potassium bromate <chem>(KBrO3)</chem>, malonic acid <chem>(CH2(COOH)2)</chem>, and manganese sulfate <chem>(MnSO4)</chem> prepared in a heated solution with sulfuric acid <chem>(H2SO4)</chem> as solvent.

其中最著名的反应是 BZ 反应，它是在硫酸 </chem > (H2SO4) </chem > (H2SO4) </chem > (CH2(COOH)2) </chem > 和用硫酸 </chem > (MnSO4) </chem > 加热溶液中制得的混合溴酸钾。

leading to an oscillation of the system. Unlike the Lotka-Volterra equation, the oscillations of the Brusselator do not depend on the amount of reactant present initially. Instead, after sufficient time, the oscillations approach a [[limit cycle]].<ref>{{cite web

|url=http://www.math.ohio-state.edu/~ault/Papers/Brusselator.pdf

|title=Archived copy

Another autocatalytic system is one driven by light coupled to photo-polymerization reactions. In a process termed optical autocatalysis, positive feedback is created between light intensity and photo-polymerization rate, via polymerization-induced increases in the refractive index. Light's preference to occupy regions of higher refractive index results in leakage of light into regions of higher molecular weight, thereby amplifying the photo-chemical reaction. The positive feedback may be expressed as:

另一种自催化体系是由光与光聚合反应耦合驱动的体系。在一个被称为光学自催化的过程中，光强度和光聚合速率之间产生正反馈，通过聚合诱导增加折射率。光喜欢占据折射率较高的区域，导致光线泄漏到分子量较高的区域，从而放大了光化学反应。积极的反馈可以表示为:

|accessdate=2015-10-15

|url-status=dead

<math>\text{polymerization rate} \to \text{molecular weight}/\text{refractive index} \to \text{intensity}</math>

文本{分子量}/文本{折射率}到文本{密度}

|archiveurl=https://web.archive.org/web/20081217020941/http://www.math.ohio-state.edu/~ault/Papers/Brusselator.pdf

|archivedate=2008-12-17

Noting that photo-polymerization rate is proportional to intensity and that refractive index is proportional to molecular weight, the positive feedback between intensity and photo-polymerization establishes the auto-catalytic behavior. Optical auto-catalysis has been shown to result on spontaneous pattern formation in photopolymers. Hosein and co-workers discovered that optical autocatalysis can also occur in photoreactive polymer blends, and that the process can induce binary phase morphologies with the same pattern as the light profile. Glycolysis consists of the degradation of one molecule of glucose and the overall production of two molecules of ATP. The process is therefore of great importance to the energetics of living cells. The global glycolysis reaction involves glucose, ADP, NAD, pyruvate, ATP, and NADH.

注意到光聚合速率与强度成正比，折射率与分子量成正比，强度与光聚合之间的正反馈建立了自催化行为。光学自催化已被证明是光聚合物自发形成图案的原因。Hosein和他的合作者发现，光学自催化也可以发生在光反应聚合物共混物中，这一过程可以诱导形成与光型相同的二元相形态。糖酵解是由一个葡萄糖分子的降解和两个 ATP 分子的全部产生组成。因此，这个过程对活细胞的能量学来说是非常重要的。糖酵解反应包括葡萄糖、 ADP、 NAD、丙酮酸、 ATP 和 NADH。

}} Dynamics of the Brusselator

</ref>

<chem>glucose{} + 2ADP{} + 2P_\mathit{i}{} + 2NAD -> 2(pyruvate){} + 2ATP{} + 2NADH</chem>.

< chem > glucose {} + 2ADP {} + 2P _ mathit { i }{} + 2NAD-> 2(丙酮酸盐){} + 2ATP {} + 2NADH </chem > 。

===Spatial order空间秩序===

The details of the process are quite involved, however, a section of the process is autocatalyzed by phosphofructokinase (PFK). This portion of the process is responsible for oscillations in the pathway that lead to the process oscillating between an active and an inactive form. Thus, the autocatalytic reaction can modulate the process.

该过程的细节相当复杂，然而，该过程的一部分是由磷酸果糖激酶(PFK)自催化的。这部分的过程负责振荡的路径，导致过程之间的振荡活跃和非活跃的形式。因此，自催化反应可以调节这一过程。

An idealized example of spatial [[spontaneous symmetry breaking]] is the case in which we have two boxes of material separated by a permeable membrane so that material can [[diffusion|diffuse]] between the two boxes. It is assumed that identical Brusselators are in each box with nearly identical initial conditions. (see Prigogine reference)

:<math>{d \over dt}[ X_1 ] = [A ] + [ X _1]^2 [Y_1 ] - [B ] [X_1 ] - [X_1 ] + D_x\left( X_2 - X_1 \right)\,</math>

It is possible to use the results from an autocatalytic reaction coupled with reaction–diffusion system theory to tailor the design of a thin layer. The autocatalytic process allows controlling the nonlinear behavior of the oxidation front, which is used to establish the initial geometry needed to generate the arbitrary final geometry. It has been successfully done in the wet oxidation of <math>Al_xGa_{1-x}As</math> to obtain arbitrary shaped layers of <math>AlO_x</math>.

利用自催化反应结合反应扩散系统理论的结果来设计薄层是可能的。自催化过程允许控制氧化前沿的非线性行为，用于建立生成任意最终几何所需的初始几何。在湿式氧化法中，成功地获得了任意形状的氧化铝层。

:<math>{d \over dt}[ Y_1 ] = [B ] [X_1 ] - [ X_1 ]^2 [Y_1 ] + D_y\left( Y_2 - Y_1\right) \,</math>

:<math>{d \over dt}[ X_2 ] = [A ] + [ X _2]^2 [Y_2 ] - [B ] [X_2 ] - [X_2 ] + D_x\left( X_1 - X_2 \right)\,</math>

The initial amounts of reactants determine the distance from a chemical equilibrium of the system. The greater the initial concentrations the further the system is from equilibrium. As the initial concentration increases, an abrupt change in order occurs. This abrupt change is known as phase transition. At the phase transition, fluctuations in macroscopic quantities, such as chemical concentrations, increase as the system oscillates between the more ordered state (lower entropy, such as ice) and the more disordered state (higher entropy, such as liquid water). Also, at the phase transition, macroscopic equations, such as the rate equations, fail. Rate equations can be derived from microscopic considerations. The derivations typically rely on a mean field theory approximation to microscopic dynamical equations. Mean field theory breaks down in the presence of large fluctuations (see Mean field theory article for a discussion). Therefore, since large fluctuations occur in the neighborhood of a phase transition, macroscopic equations, such as rate equations, fail. As the initial concentration increases further, the system settles into an ordered state in which fluctuations are again small. (see Prigogine reference)

反应物的初始量决定了与体系化学平衡的距离。初始浓度越大，系统离平衡越远。随着初始浓度的增加，顺序发生突变。这种突变被称为相变。在相变阶段，宏观量的波动，如化学浓度，随着系统在更有序的状态（低熵，如冰）和更无序的状态（更高的熵，如液态水）之间振荡而增加。同样，在相变过程中，宏观方程，如速率方程，会失效。速率方程可以从微观角度推导出来。推导通常依赖于对微观动力学方程的平均场理论近似。平均场理论在大波动的存在下会崩溃（见平均场理论文章的讨论）。因此，由于大的波动发生在相变附近，例如速率方程等的宏观方程便失灵了。随着初始浓度的进一步增加，系统进入有序状态，在这种状态下波动又很小(见 Prigogine 参考文献)

:<math>{d \over dt}[ Y_2 ] = [B ] [X_2 ] - [ X_2 ]^2 [Y_2 ] + D_y\left( Y_1 - Y_2\right) \,</math>

Here, the numerical subscripts indicate which box the material is in. There are additional terms proportional to the diffusion coefficient D that account for the exchange of material between boxes.

在这里，数字下标表示材料在哪个盒子里。还有一些与扩散系数D成比例的附加项，它们解释了盒子之间的物质交换。

Asymmetric autocatalysis occurs when the reaction product is chiral and thus acts as a chiral catalyst for its own production. Reactions of this type, such as the Soai reaction, have the property that they can amplify a very small enantiomeric excess into a large one. This has been proposed as an important step in the origin of biological homochirality.

不对称自催化反应发生在反应产物是手性的情况下，因此可以作为手性催化剂自身生产。这种类型的反应，比如 Soai 反应，具有将非常小的对映体过量百分数放大成大的反应的特性。这被认为是生物同手性起源的重要步骤。

If the system is initiated with the same conditions in each box, then a small fluctuation will lead to separation of materials between the two boxes. One box will have a predominance of X, and the other will have a predominance of Y.
如果系统在每个箱子的相同条件下启动，那么小的波动将导致两个箱子之间的物料分离。一个方框的优势是X，另一个方框的优势是Y。

==Real examples实例==

Real examples of [[clock reaction]]s are the [[Belousov–Zhabotinsky reaction]] (BZ reaction), the [[Briggs–Rauscher reaction]], the [[Bray–Liebhafsky reaction]] and the [[iodine clock reaction]]. These are oscillatory reactions, and the concentration of products and reactants can be approximated in terms of [[damping|damped]] [[oscillation]]s.
时钟反应]]的真正例子是[[Belousov–Zhabotinsky reaction]]（BZ反应）、[[Briggs–Rauscher 反应]]、[[Bray–Liebhafsky 反应]]和[[碘钟反应]]。这些都是振荡反应，产物和反应物的浓度可以用阻尼，振荡来近似。
In 1995 Stuart Kauffman proposed that life initially arose as autocatalytic chemical networks.

1995年，Stuart Kauffman提出生命最初是以自催化化学网络的形式出现的。

The best-known reaction, the BZ reaction, can be created with a mixture of potassium bromate <chem>(KBrO3)</chem>, malonic acid <chem>(CH2(COOH)2)</chem>, and manganese sulfate <chem>(MnSO4)</chem> prepared in a heated solution with sulfuric acid <chem>(H2SO4)</chem> as solvent.<ref>{{Cite web|url=http://online.redwoods.cc.ca.us/instruct/darnold/deproj/Sp98/Gabe/|title=The Belousov-Zhabotinsky Reaction|last=Peterson|first=Gabriel|date=|website=|accessdate=|archiveurl=https://web.archive.org/web/20121231011212/http://online.redwoods.cc.ca.us/instruct/darnold/deproj/Sp98/Gabe/|archivedate=December 31, 2012}}</ref>

British ethologist Richard Dawkins wrote about autocatalysis as a potential explanation for abiogenesis in his 2004 book The Ancestor's Tale. He cites experiments performed by Julius Rebek and his colleagues at the Scripps Research Institute in California in which they combined amino adenosine and pentafluorophenyl ester with the autocatalyst amino adenosine triacid ester (AATE). One system from the experiment contained variants of AATE which catalyzed the synthesis of themselves. This experiment demonstrated the possibility that autocatalysts could exhibit competition within a population of entities with heredity, which could be interpreted as a rudimentary form of natural selection, and that certain environmental changes (such as irradiation) could alter the chemical structure of some of these self-replicating molecules (an analog for mutation) in such ways that could either boost or interfere with its ability to react, thus boosting or interfering with its ability to replicate and spread in the population.

英国动物行为学家 Richard Dawkins在他2004年出版的《祖先的故事》一书中提到了自我催化作为自然发生的潜在解释。他引用了 Julius Rebek 和他的同事们在加利福尼亚斯克里普斯研究所进行的实验，他们将氨基腺苷和五氟苯酯与氨基腺苷三酸酯(AATE)结合在一起。实验中的一个系统包含了催化自身合成的 AATE 的变体。这项实验证明了这样一种可能性，即自动催化剂可以在具有遗传性的实体群体中展现竞争，这可以被解释为一种基本的自然选择形式，而且某些环境变化(如辐照)可以改变某些自我复制分子(变异的类似物)的化学结构，这种方式可以增强或干扰其反应能力，从而增强或干扰其复制和在群体中传播的能力。

== Optics example光学实例 ==

Autocatalysis plays a major role in the processes of life. Two researchers who have emphasized its role in the origins of life are Robert Ulanowicz and Stuart Kauffman.

自动催化在生命过程中起着重要的作用。强调其在生命起源中的作用的两位研究人员是Robert Ulanowicz和Stuart Kauffman。

Another autocatalytic system is one driven by light coupled to photo-polymerization reactions. In a process termed optical autocatalysis, positive feedback is created between light intensity and photo-polymerization rate, via polymerization-induced increases in the refractive index. Light's preference to occupy regions of higher refractive index results in leakage of light into regions of higher molecular weight, thereby amplifying the photo-chemical reaction. The positive feedback may be expressed as:<ref name=":0">{{Cite journal|last=Biria|first=Saeid|last2=Malley|first2=Phillip P. A.|last3=Kahan|first3=Tara F.|last4=Hosein|first4=Ian D.|date=2016-11-15|title=Optical Autocatalysis Establishes Novel Spatial Dynamics in Phase Separation of Polymer Blends during Photocuring|journal=ACS Macro Letters|volume=5|issue=11|pages=1237–1241|doi=10.1021/acsmacrolett.6b00659}}</ref>

Autocatalysis occurs in the initial transcripts of rRNA. The introns are capable of excising themselves by the process of two nucleophilic transesterification reactions. The RNA able to do this is sometimes referred to as a ribozyme. Additionally, the citric acid cycle is an autocatalytic cycle run in reverse.

自我催化发生在RNA的最初转录本中。这些内含子能够通过两个亲核酯交换反应反应自我激活。能够做到这一点的 RNA 有时被称为核酶。此外，三羧酸循环是一种反向运行的自动催化循环。

:<math>\text{polymerization rate} \to \text{molecular weight}/\text{refractive index} \to \text{intensity}</math>

Ultimately, biological metabolism itself can be seen as a vast autocatalytic set, in that all of the molecular constituents of a biological cell are produced by reactions involving this same set of molecules.

最终，生物的新陈代谢本身可以被看作是一个巨大的自我催化装置，因为一个生物细胞的所有分子成分都是由包含同一组分子的反应产生的。

Noting that photo-polymerization rate is proportional to intensity<ref>{{Cite journal|last=Decker|first=Christian|date=1998-02-01|title=The use of UV irradiation in polymerization|url=|journal=Polymer International|language=en|volume=45|issue=2|pages=133–141 |doi=10.1002/(SICI)1097-0126(199802)45:2<133::AID-PI969>3.0.CO;2-F}}</ref> and that refractive index is proportional to molecular weight,<ref>{{Cite journal|last=Askadskii|first=A. A.|year=1990|title=Influence of crosslinking density on the properties of polymer networks|journal=Polymer Science U.S.S.R.|volume=32|issue=10|pages=2061–2069|doi=10.1016/0032-3950(90)90361-9}}</ref> the positive feedback between intensity and photo-polymerization establishes the auto-catalytic behavior. Optical auto-catalysis has been shown to result on spontaneous [[pattern formation]] in photopolymers.<ref>{{Cite journal|last=Burgess|first=Ian B.|last2=Shimmell|first2=Whitney E.|last3=Saravanamuttu|first3=Kalaichelvi|date=2007-04-01|title=Spontaneous Pattern Formation Due to Modulation Instability of Incoherent White Light in a Photopolymerizable Medium|journal=Journal of the American Chemical Society|volume=129|issue=15|pages=4738–4746|doi=10.1021/ja068967b|pmid=17378567|issn=0002-7863}}</ref><ref>{{Cite journal|last=Basker|first=Dinesh K.|last2=Brook|first2=Michael A.|last3=Saravanamuttu|first3=Kalaichelvi|title=Spontaneous Emergence of Nonlinear Light Waves and Self-Inscribed Waveguide Microstructure during the Cationic Polymerization of Epoxides|journal=The Journal of Physical Chemistry C|language=en|volume=119|issue=35|pages=20606–20617|doi=10.1021/acs.jpcc.5b07117|year=2015}}</ref><ref>{{Cite journal|last=Biria|first=Saeid|last2=Malley|first2=Philip P. A.|last3=Kahan|first3=Tara F.|last4=Hosein|first4=Ian D.|date=2016-03-03|title=Tunable Nonlinear Optical Pattern Formation and Microstructure in Cross-Linking Acrylate Systems during Free-Radical Polymerization|journal=The Journal of Physical Chemistry C|volume=120|issue=8|pages=4517–4528|doi=10.1021/acs.jpcc.5b11377|issn=1932-7447}}</ref> Hosein and co-workers discovered that optical autocatalysis can also occur in photoreactive polymer blends, and that the process can induce binary phase morphologies with the same pattern as the light profile.<ref name=":0" /> The light undergoes optical [[Modulational instability|modulation instability]], spontaneous dividing into a multitude of optical filaments, and the polymer system thereby forms filaments within the blend structure.<ref name=":0" /> The result is a new system that couples optical autocatalytic behavior to [[spinodal decomposition]].
注意到光聚合速率与强度成正比，折射率与分子量成正比，强度和光聚合之间的正反馈建立了自催化行为。光自催化已经被证明可以导致光聚合物中自发图案的形成。Hosein和他的同事发现，光自催化也可以发生在光活性聚合物混合物中，并且该过程可以诱导具有与光轮廓相同图案的二元相形态。光经历了光调制不稳定性，自发地分裂成许多光学细丝，因此，聚合物系统在共混结构中形成细丝。结果是一个将光学自催化行为与旋节分解相耦合的新系统。

==Biological example生物实例==

It is known that an important metabolic cycle, [[glycolysis]], displays temporal order.<ref>{{cite book | author=G. Nicolis and [[Ilya Prigogine]] | title=Self-Organization in Nonequilibrium Systems | location= New York | publisher=John Wiley and Sons| year=1977 | isbn=978-0-471-02401-9}}

</ref> Glycolysis consists of the degradation of one molecule of glucose and the overall production of two molecules of [[Adenosine triphosphate|ATP]]. The process is therefore of great importance to the energetics of living cells. The global glycolysis reaction involves [[glucose]], [[Adenosine diphosphate|ADP]], [[Nicotinamide adenine dinucleotide|NAD]], [[Pyruvic acid|pyruvate]], [[Adenosine triphosphate|ATP]], and NADH.
糖酵解包括一个葡萄糖分子的降解和两个分子[[三磷酸腺苷| ATP]]的合成。因此，这个过程对活细胞的能量学非常重要。全局糖酵解反应涉及[[葡萄糖]]、[[二磷酸腺苷| ADP]]、[[烟酰胺腺嘌呤二核苷酸| NAD]]

:<chem>glucose{} + 2ADP{} + 2P_\mathit{i}{} + 2NAD -> 2(pyruvate){} + 2ATP{} + 2NADH</chem>.

The details of the process are quite involved, however, a section of the process is autocatalyzed by [[phosphofructokinase]] (PFK). This portion of the process is responsible for oscillations in the pathway that lead to the process oscillating between an active and an inactive form. Thus, the autocatalytic reaction can modulate the process.

过程的细节是相当复杂的，然而，过程的一部分是由[[磷酸果糖激酶]]（PFK）自动催化的。这个过程的这一部分负责路径中的振荡，导致过程在一个活跃的和一个不活跃的形式之间振荡。因此，自催化反应可以调节这一过程。

==Shape tailoring of thin layers薄层剪裁==

It is possible to use the results from an autocatalytic reaction coupled with [[reaction–diffusion system]] theory to tailor the design of a thin layer. The autocatalytic process allows controlling the nonlinear behavior of the oxidation [[Front (physics)|front]], which is used to establish the initial geometry needed to generate the arbitrary final geometry.<ref>{{cite journal |last1=Alfaro-Bittner |first1=K. |last2=Rojas |first2=R.G. |last3=Lafleur |first3=G. |last4=Calvez |first4=S. |last5=Almuneau |first5=G. |last6=Clerc |first6=M.G. |last7=Barbay |first7=S. |title=Modeling the Lateral Wet Oxidation of into Arbitrary Mesa Geometries |journal=Physical Review Applied|date=22 April 2019|volume=11 |issue=4|page=044067|doi=10.1103/PhysRevApplied.11.044067|url=https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.11.044067}}</ref> It has been successfully done in the wet oxidation of <math>Al_xGa_{1-x}As</math> to obtain arbitrary shaped layers of <math>AlO_x</math>.
利用自催化反应与[[反应-扩散系统]]理论相结合的结果，可以定制薄层的设计。自动催化过程允许控制氧化的非线性行为，用于建立生成任意最终几何体所需的初始几何体

==Phase transitions相变==

The initial amounts of reactants determine the distance from a chemical equilibrium of the system. The greater the initial concentrations the further the system is from equilibrium. As the initial concentration increases, an abrupt change in [[entropy|order]] occurs. This abrupt change is known as [[phase transition]]. At the phase transition, fluctuations in macroscopic quantities, such as chemical concentrations, increase as the system oscillates between the more ordered state (lower entropy, such as ice) and the more disordered state (higher entropy, such as liquid water). Also, at the phase transition, macroscopic equations, such as the rate equations, fail. Rate equations can be derived from microscopic considerations. The derivations typically rely on a [[mean field theory]] approximation to microscopic dynamical equations. Mean field theory breaks down in the presence of large fluctuations (see [[Mean field theory]] article for a discussion). Therefore, since large fluctuations occur in the neighborhood of a phase transition, macroscopic equations, such as rate equations, fail. As the initial concentration increases further, the system settles into an ordered state in which fluctuations are again small. (see Prigogine reference)

反应物的初始量决定了与体系化学平衡的距离。初始浓度越大，系统离平衡越远。随着初始浓度的增加，[[熵|阶]]发生突变。这种突变被称为[[相变]]。在相变阶段，宏观量的波动，如化学浓度，随着系统在更有序的状态（低熵，如冰）和更无序的状态（更高的熵，如液态水）之间振荡而增加。同样，在相变过程中，宏观方程，如速率方程，会失效。速率方程可以从微观角度推导出来。推导通常依赖于对微观动力学方程的[[平均场理论]]近似。平均场理论在大波动的情况下会崩溃（见[[平均场理论]]文章进行讨论）。因此，由于大的波动发生在相变附近，宏观方程，如速率方程，失败了。随着初始浓度的进一步增加，系统进入有序状态，在这种状态下波动又很小。（见Prigogine参考文献）

==Asymmetric autocatalysis不对称自催化 ==

Asymmetric autocatalysis occurs when the reaction product is [[chiral]] and thus acts as a chiral catalyst for its own production. Reactions of this type, such as the [[Soai reaction]], have the property that they can amplify a very small [[enantiomeric excess]] into a large one. This has been proposed as an important step in the origin of biological [[homochirality]].<ref name="Soai2001">{{cite journal|vauthors=Soai K, Sato I, Shibata T | title=Asymmetric autocatalysis and the origin of chiral homogeneity in organic compounds. | journal=The Chemical Record | year= 2001 | volume= 1 | issue= 4 | pages= 321–32 | pmid=11893072 | doi= 10.1002/tcr.1017| pmc= }}</ref>
非对称自催化发生在反应产物为[[手性]]时，因此作为手性催化剂进行自身生产。这种类型的反应，如[[Soai反应]]，具有将很小的[[对映体过量]]放大为大反应的性质。在这一点上，手性被认为是生物起源的一个重要步骤

== Role in origin of life生命起源中的角色 ==

{{main|Abiogenesis}}

In 1995 [[Stuart Kauffman]] proposed that life initially arose as autocatalytic chemical networks.<ref>{{cite book|author=Stuart Kauffman|title=At Home in the Universe: The Search for the Laws of Self-Organization and Complexity|isbn=978-0-19-509599-9|publisher=Oxford University Press|year=1995|url-access=registration|url=https://archive.org/details/athomeinuniverse00kauf_0}}</ref>
1995年[[Stuart Kauffman]]提出生命最初是以自催化化学网络的形式出现的

Category:Catalysis

类别: 催化

<noinclude>

This page was moved from [[wikipedia:en:Autocatalysis]]. Its edit history can be viewed at [[自催化/edithistory]]</noinclude>

[[Category:待整理页面]]

自催化

2020-12-02T04:10:56Z

Yetmings：

此词条暂由Henry 翻译。

{{more citations needed|date=September 2010}}

A single [[chemical reaction]] is said to be '''autocatalytic''' if one of the reaction products is also a [[catalyst]] for the same or a coupled reaction.<ref name=Steinfeld>Steinfeld J.I., Francisco J.S. and Hase W.L. ''Chemical Kinetics and Dynamics'' (2nd ed., Prentice-Hall 1999) p.151-2 {{ISBN|0-13-737123-3}}</ref> Such a reaction is called an '''autocatalytic reaction'''.

A single chemical reaction is said to be autocatalytic if one of the reaction products is also a catalyst for the same or a coupled reaction. Such a reaction is called an autocatalytic reaction.

一个单一的化学反应，如果其中一个反应产物也是同一反应或耦合反应的催化剂，则称为具有自催化性质。这种反应称为 自催化反应autocatalytic reaction。

A ''set'' of chemical reactions can be said to be "collectively autocatalytic" if a number of those reactions produce, as reaction products, catalysts for enough of the other reactions that the entire set of chemical reactions is self-sustaining given an input of energy and food molecules (see [[autocatalytic set]]).

A set of chemical reactions can be said to be "collectively autocatalytic" if a number of those reactions produce, as reaction products, catalysts for enough of the other reactions that the entire set of chemical reactions is self-sustaining given an input of energy and food molecules (see autocatalytic set).

如果一系列化学反应作为反应产物产生足够多的其他反应的催化剂，使整套化学反应在能量和食物分子输入的情况下能够自我维持，则可以说这些化学反应是”集体自我催化”的。

==Chemical reactions化学反应==

{{main|Chemical reaction|Chemical kinetics}}

A chemical reaction of two reactants and two products can be written as

A chemical reaction of two reactants and two products can be written as

两种反应物和两种产物的化学反应可以写成

:<math> \alpha A + \beta B \rightleftharpoons \sigma S + \tau T</math>

<math> \alpha A + \beta B \rightleftharpoons \sigma S + \tau T</math>

where the Greek letters are [[stoichiometric coefficients]] and the capital Latin letters represent chemical species. The chemical reaction proceeds in both the forward and reverse direction. This equation is easily generalized to any number of reactants, products, and reactions.

where the Greek letters are stoichiometric coefficients and the capital Latin letters represent chemical species. The chemical reaction proceeds in both the forward and reverse direction. This equation is easily generalized to any number of reactants, products, and reactions.

其中希腊字母是化学计量系数，大写拉丁字母代表化学物种。化学反应在正向和反向两个方向进行。这个方程可以很容易地推广到任意数量的反应物、产物和反应。

===Chemical equilibrium化学平衡===

In [[chemical equilibrium]] the forward and reverse [[reaction rate]]s are such that each chemical species is being created at the same rate it is being destroyed. In other words, the rate of the forward reaction is equal to the rate of the reverse reaction.

In chemical equilibrium the forward and reverse reaction rates are such that each chemical species is being created at the same rate it is being destroyed. In other words, the rate of the forward reaction is equal to the rate of the reverse reaction.

在化学平衡状态，正向和反向的反应速率是这样的情况：每一种化学物质都以同样的速率生成和消失。换句话说，正向反应的速率等于反向反应的速率。

:<math> k_+ [ A ]^\alpha [B ]^\beta = k_{-} [S ]^\sigma[T ]^\tau \,</math>

<math> k_+ [ A ]^\alpha [B ]^\beta = k_{-} [S ]^\sigma[T ]^\tau \,</math>

K _ + [ a ] ^ alpha [ b ] ^ beta = k _ {-}[ s ] ^ sigma [ t ] ^ tau，</math >

Here, the brackets indicate the concentration of the chemical species, in [[mole (unit)|moles]] per liter, and k+ and k− are [[rate constant]]s.

Here, the brackets indicate the concentration of the chemical species, in moles per liter, and k+ and k− are rate constants.

这里，括号表示化学物质的浓度，以摩尔/升为单位，k+和 k-是速率常数。

===Far from equilibrium远离平衡态===

Far from equilibrium, the forward and reverse reaction rates no longer balance and the concentration of reactants and products is no longer constant. For every forward reaction <math>\alpha </math> molecules of A are destroyed. For every reverse reaction <math>\alpha </math> molecules of A are created. In the case of an [[elementary reaction]] step the [[reaction order]] in each direction equals the molecularity, so that the rate of change in the number of moles of A is then

Far from equilibrium, the forward and reverse reaction rates no longer balance and the concentration of reactants and products is no longer constant. For every forward reaction <math>\alpha </math> molecules of A are destroyed. For every reverse reaction <math>\alpha </math> molecules of A are created. In the case of an elementary reaction step the reaction order in each direction equals the molecularity, so that the rate of change in the number of moles of A is then

在远离平衡态时，正向和反向反应速率不再是平衡的，反应物和产物的浓度不再是恒定的。对于每一个前向反应，a 的分子会消失。对于每一个逆反应，a 的分子都会被产生出来。在基本反应步骤中，每个方向的反应级数等于“反应分子数”（molecularity），因此 a 的摩尔数的变化率就是

:<math>{d \over dt}[ A ] =-\alpha k_+ [ A ]^\alpha [B ]^\beta +\alpha k_{-} [S ]^\sigma[T ]^\tau \,</math>

<math>{d \over dt}[ A ] =-\alpha k_+ [ A ]^\alpha [B ]^\beta +\alpha k_{-} [S ]^\sigma[T ]^\tau \,</math>

[ a ] =-alpha k _ + [ a ] ^ alpha [ b ] ^ beta + alpha k _ {-}[ s ] ^ sigma [ t ] ^ tau，</math >

:<math>{d \over dt}[ B ] =-\beta k_+ [ A ]^\alpha [B ]^\beta +\beta k_{-} [S ]^\sigma[T ]^\tau \,</math>

<math>{d \over dt}[ B ] =-\beta k_+ [ A ]^\alpha [B ]^\beta +\beta k_{-} [S ]^\sigma[T ]^\tau \,</math>

[ b ] =-beta k _ + [ a ] ^ alpha [ b ] ^ beta + beta k _ {-}[ s ] ^ sigma [ t ] ^ tau，</math >

:<math>{d \over dt}[ S ] =\sigma k_+ [ A ]^\alpha [B ]^\beta -\sigma k_{-} [S ]^\sigma[T ]^\tau \,</math>

<math>{d \over dt}[ S ] =\sigma k_+ [ A ]^\alpha [B ]^\beta -\sigma k_{-} [S ]^\sigma[T ]^\tau \,</math>

[ s ] = sigma k _ + [ a ] ^ alpha [ b ] ^ beta-sigma k _ {-}[ s ] ^ sigma [ t ] ^ tau，</math >

:<math>{d \over dt}[ T ] =\tau k_+ [ A ]^\alpha [B ]^\beta -\tau k_{-} [S ]^\sigma[T ]^\tau \,</math>

<math>{d \over dt}[ T ] =\tau k_+ [ A ]^\alpha [B ]^\beta -\tau k_{-} [S ]^\sigma[T ]^\tau \,</math>

[ t ] = tau k _ + [ a ] ^ alpha [ b ] ^ beta-tau k _ {-}[ s ] ^ sigma [ t ] ^ tau，</math >

This system of equations has a single stable [[Fixed point (mathematics)|fixed point]] when the forward rates and the reverse rates are equal (when <math>{d \over dt}=0</math> for every species). This means that the system evolves to the equilibrium state, and this is the only state to which it evolves.<ref>{{cite journal |last1=Ross |first1=John |last2=Garcia-Colin |first2=Leopoldo S. |title=Thermodynamics of chemical systems far from equilibrium |journal=The Journal of Physical Chemistry |date=March 1989 |volume=93 |issue=5 |pages=2091–2092 |doi=10.1021/j100342a075}}</ref>

This system of equations has a single stable fixed point when the forward rates and the reverse rates are equal (when <math>{d \over dt}=0</math> for every species). This means that the system evolves to the equilibrium state, and this is the only state to which it evolves.

这个系统的方程组有一个单一的稳定不动点解，这个解的情况就是每个物种的正向速率和反向速率相等。这意味着这个系统是往平衡状态演化，而且这个平衡状态这是系统演化到的唯一状态。

===Autocatalytic reactions自催化反应===

[[Image:Sigmoid curve for an autocatalytical reaction.jpg|256px|right|thumb|Sigmoid variation of product concentration in autocatalytic reactions]]

Sigmoid variation of product concentration in autocatalytic reactions

自催化反应中产物浓度的 s 形变化

Autocatalytic reactions are those in which at least one of the products is a reactant. Perhaps the simplest autocatalytic reaction can be written<ref name=Steinfeld/>

Autocatalytic reactions are those in which at least one of the products is a reactant. Perhaps the simplest autocatalytic reaction can be written

自催化反应是那些其中至少一个产物是反应物的反应。也许最简单的自催化反应可以这样写出来

:<math> A + B \rightleftharpoons 2B</math>

<math>[A]=\frac{[A]_0+[B]_0}{1+\frac{[B]_0}{[A]_0}e^{([A]_0+[B]_0)kt}}</math>

< math > [ a ] = frac {[ a ] _ 0 + [ b ] _ 0}{1 + frac {[ b ] _ 0}{[ a ] _ 0} e ^ {(([ a ] _ 0 + [ b ] _ 0) kt }} </math >

and

及

with the rate equations (for an elementary reaction)

<math>[B]=\frac{[A]_0+[B]_0}{1+\frac{[A]_0}{[B]_0}e^{-([A]_0+[B]_0)kt}}</math>.

< math > [ b ] = frac {[ a ] _ 0 + [ b ] _ 0}{1 + frac {[ a ] _ 0}{[ b ] _ 0} e ^ {-([ a ] _ 0 + [ b ] _ 0) kt }} </math > .

:<math>{d \over dt}[ A ] =- k_+ [ A ] [B ] + k_{-} [B ]^2 \,</math>

The graph for these equations is a sigmoid curve (specifically a logistic function), which is typical for autocatalytic reactions: these chemical reactions proceed slowly at the start (the induction period) because there is little catalyst present, the rate of reaction increases progressively as the reaction proceeds as the amount of catalyst increases and then it again slows down as the reactant concentration decreases. If the concentration of a reactant or product in an experiment follows a sigmoid curve, the reaction may be autocatalytic.

这些方程的曲线图是一条s形曲线（特别是logistic函数），这是自催化反应的典型特征：这些化学反应在开始时（诱导期）进行得很慢，因为几乎没有催化剂存在，随着催化剂用量的增加，反应速度逐渐增加，然后随着反应物浓度的降低，反应速度再次减慢。如果一个实验中反应物或产物的浓度服从s形曲线，则该反应可能是自催化的。

:<math>{d \over dt}[ B ] = + k_+ [ A ] [B ] -k_{-} [B ]^2 \,</math>.

These kinetic equations apply for example to the acid-catalyzed hydrolysis of some esters to carboxylic acids and alcohols. In the hurricane example, hurricanes are formed from unequal heating within the atmosphere. The Earth's atmosphere is then far from thermal equilibrium. The order of the Earth's atmosphere increases, but at the expense of the order of the sun. The sun is becoming more disorderly as it ages and throws off light and material to the rest of the universe. The total disorder of the sun and the earth increases despite the fact that orderly hurricanes are generated on earth.

这些动力学方程适用于一些酯的酸催化水解为羧酸和醇。在飓风的例子中，飓风是由大气中不均匀的加热形成的。地球的大气层离热平衡还很远。地球大气的秩序增加了，但以太阳的秩序为代价。随着年龄的增长，太阳正变得越来越无序，并向宇宙的其他部分发射光和物质。尽管有秩序的飓风随时都会发生，但太阳和地球的整体混乱程度却在增加。

This reaction is one in which a molecule of species A interacts with a molecule of species B. The A molecule is converted into a B molecule. The final product consists of the original B molecule plus the B molecule created in the reaction.

这个反应是物种A的分子与物种B的分子相互作用，A分子转化为B分子。最终产物由原始的B分子加上反应中产生的B分子组成。

A similar example exists for living chemical systems. The sun provides energy to green plants. The green plants are food for other living chemical systems. The energy absorbed by plants and converted into chemical energy generates a system on earth that is orderly and far from chemical equilibrium. Here, the difference from chemical equilibrium is determined by an excess of reactants over the equilibrium amount. Once again, order on earth is generated at the expense of entropy increase of the sun. The total entropy of the earth and the rest of the universe increases, consistent with the Second Law.

类似的例子也存在于活的化学系统中。太阳为绿色植物提供能量。绿色植物是其他生命化学系统的食物。植物吸收并转化为化学能的能量在地球上形成了一个有序的系统，这个系统远离化学平衡。在这里，反应物超过平衡量决定了化学平衡的差异。再一次，地球上的秩序是以太阳的熵增为代价而产生的。地球和宇宙其余部分的总熵增加，符合第二定律。

The key feature of these rate equations is that they are [[nonlinear]]; the second term on the right varies as the square of the concentration of B. This feature can lead to multiple fixed points of the system, much like a [[quadratic equation]] can have multiple roots. Multiple fixed points allow for multiple states of the system. A system existing in multiple [[macroscopic]] states is more orderly (has lower entropy) than a system in a single state.
这些速率方程的关键特征是它们是[[非线性]；右边的第二项随B浓度的平方而变化。这一特性可导致系统的多个不动点，就像[[二次方程]]可以有多个根一样。多个固定点允许系统的多种状态。存在于多个[[宏观]]状态的系统比处于单一状态的系统更有序（熵更低）。

Some autocatalytic reactions also generate order in a system at the expense of its surroundings. For example, (clock reactions) have intermediates whose concentrations oscillate in time, corresponding to temporal order. Other reactions generate spatial separation of chemical species corresponding to spatial order. More complex reactions are involved in metabolic pathways and metabolic networks in biological systems.

一些自催化反应也以牺牲周围环境为代价，在系统中产生有序。例如，(时钟反应)有其浓度在时间上振荡的中间体，对应于时间顺序。其他反应产生空间分离的化学物质对应的空间秩序。更复杂的反应涉及到生物系统中的代谢途径和代谢网络。

The concentrations of A and B vary in time according to<ref name=Steinfeld/><ref name=Moore>Moore J.W. and [[Ralph Pearson|Pearson R.G.]] ''Kinetics and Mechanism'' (John Wiley 1981) p.26 {{ISBN|0-471-03558-0}}</ref>

:<math>[A]=\frac{[A]_0+[B]_0}{1+\frac{[B]_0}{[A]_0}e^{([A]_0+[B]_0)kt}}</math>

The transition to order as the distance from equilibrium increases is not usually continuous. Order typically appears abruptly. The threshold between the disorder of chemical equilibrium and order is known as a phase transition. The conditions for a phase transition can be determined with the mathematical machinery of non-equilibrium thermodynamics.

随着离平衡距离的增加，向有序的过渡通常是不连续的。秩序通常会突然出现。化学平衡和有序之间的无序阈值被称为相变。相变的条件可以用非平衡态热力学的数学方法来确定。

and

:<math>[B]=\frac{[A]_0+[B]_0}{1+\frac{[A]_0}{[B]_0}e^{-([A]_0+[B]_0)kt}}</math>.

The graph for these equations is a [[sigmoid function|sigmoid curve]] (specifically a [[logistic function]]), which is typical for autocatalytic reactions: these chemical reactions proceed slowly at the start (the [[induction period]]) because there is little catalyst present, the rate of reaction increases progressively as the reaction proceeds as the amount of catalyst increases and then it again slows down as the reactant concentration decreases. If the concentration of a reactant or product in an experiment follows a sigmoid curve, the reaction may be autocatalytic.
这些方程的图形是一个[[西格莫函数| S形曲线]]（特别是[[逻辑函数]]），这是自催化反应的典型特征：这些化学反应在开始时（诱导期]]）进行得很慢，因为催化剂很少，随着催化剂用量的增加，反应速度逐渐增加，然后随着反应物浓度的降低，反应速度再次减慢。如果一个实验中反应物或产物的浓度服从sigmoid曲线，则该反应可能是自催化的。
A chemical reaction cannot oscillate about a position of final equilibrium because the second law of thermodynamics requires that a thermodynamic system approach equilibrium and not recede from it. For a closed system at constant temperature and pressure, the Gibbs free energy must decrease continuously and not oscillate. However it is possible that the concentrations of some reaction intermediates oscillate, and also that the rate of formation of products oscillates.

一个化学反应不能在一个最终平衡位置上振荡，因为热力学第二定律需要一个接近平衡的热力学系统，而不能退出平衡位置。对于一个温度和压力恒定的封闭系统， 吉布斯自由能Gibbs free energy必须不断减小而不振荡。然而，一些反应中间体的浓度可能会振荡，产物的生成速率也可能振荡。

These kinetic equations apply for example to the acid-catalyzed hydrolysis of some [[ester]]s to [[carboxylic acid]]s and [[alcohol]]s.<ref name=Moore/> There must be at least some acid present initially to start the catalyzed mechanism; if not the reaction must start by an alternate uncatalyzed path which is usually slower. The above equations for the catalyzed mechanism would imply that the concentration of acid product remains zero forever.<ref name=Moore/>
例如，这些动力学方程适用于某些[[酯]]到[[羧酸]]和[[醇]]的酸催化水解。最初必须至少存在一些酸来启动催化机制；否则，反应必须通过通常较慢的替代非催化路径开始。上述催化机理的方程式意味着酸产物的浓度永远为零。

The Lotka–Volterra equation is [[isomorphic with the predator–prey model and the two-reaction autocatalytic model. In this example baboons and cheetahs are equivalent to two different chemical species X and Y in autocatalytic reactions.]]

方程[同构于捕食-食饵模型和双反应自催化模型。在这个例子中，狒狒和猎豹在自动催化反应中相当于两种不同的化学物种 x 和 y

==Creation of order秩序创立==

Consider a coupled set of two autocatalytic reactions in which the concentration of one of the reactants A is much larger than its equilibrium value. In this case, the forward reaction rate is so much larger than the reverse rates that we can neglect the reverse rates.

考虑一组耦合的两个自催化反应，其中一个反应物 a 的浓度远远大于其平衡值。在这种情况下，正向反应速率远远大于反向反应速率，因此我们可以忽略反向反应速率。

===Background背景===

<math> A + X \rightarrow 2X</math>

A + x 右行2X

The [[second law of thermodynamics]] states that the disorder ([[entropy]]) of a physical or chemical system and its surroundings (a [[closed system]]) must increase with time. Systems left to themselves become increasingly [[random]], and orderly energy of a system like uniform motion degrades eventually to the random motion of particles in a [[heat bath]].
[[热力学第二定律]指出，物理或化学系统及其周围环境（封闭系统）的无序度（[[熵]]）必须随时间而增加。留给自己的系统变得越来越[[随机]]，系统的有序能量（如均匀运动）最终退化为粒子在[[热浴]中的随机运动
<math> X + Y \rightarrow 2Y</math>

(数学) x + y 右行2Y

There are, however, many instances in which physical systems spontaneously become [[emergence|emergent]] or orderly. For example, despite the destruction they cause, [[hurricane]]s have a very orderly [[vortex]] motion when compared to the random motion of the air molecules in a closed room. Even more spectacular is the order created by chemical systems; the most dramatic being the order associated with life.
然而，在许多情况下，物理系统自发地变得新生或有序。例如，尽管飓风造成了破坏，但与封闭房间中空气分子的随机运动相比，[[飓风]]的运动非常有序。更引人注目的是化学系统创造的秩序；最引人注目的是与生命相关的秩序。
<math> Y \rightarrow E</math>

[数学，数学]

This is consistent with the Second Law, which requires that the total disorder of a system ''and its surroundings'' must increase with time. Order can be created in a system by an even greater decrease in order of the system's surroundings.<ref>{{cite book | author=Ilya Prigogine | title=From Being to Becoming: Time and Complexity in the Physical Sciences | location=San Francisco | publisher=W. H. Freeman | year=1980 | isbn=978-0-7167-1107-0 | author-link=Ilya Prigogine | url-access=registration | url=https://archive.org/details/frombeingtobecom00ipri }}
这与第二定律是一致的，第二定律要求系统“及其周围环境”的整体无序程度必须随时间而增加。在一个系统中，秩序可以通过系统周围环境的更大程度的降低而产生
with the rate equations

用速率方程式

</ref> In the hurricane example, hurricanes are formed from unequal heating within the atmosphere. The Earth's atmosphere is then far from [[thermal equilibrium]]. The order of the Earth's atmosphere increases, but at the expense of the order of the sun. The sun is becoming more disorderly as it ages and throws off light and material to the rest of the universe. The total disorder of the sun and the earth increases despite the fact that orderly hurricanes are generated on earth.

在飓风的例子中，飓风是由大气中不均匀的加热形成的。地球的大气层离[[热平衡]]很远。地球大气的秩序增加了，但以太阳的秩序为代价。随着年龄的增长，太阳正变得越来越无序，并向宇宙的其他部分发射光和物质。尽管地球上产生了有序的飓风，但太阳和地球的总体混乱程度却在增加。

<math>{d \over dt}[ X ] = k_1 [ A ] [X ] - k_{2} [X ][Y ] \,</math>

< math > { d over dt }[ x ] = k_1[ a ][ x ]-k_2}[ x ][ y ] ，</math >

A similar example exists for living chemical systems. The sun provides energy to green plants. The green plants are food for other living chemical systems. The energy absorbed by plants and converted into chemical energy generates a system on earth that is orderly and far from [[chemical equilibrium]]. Here, the difference from chemical equilibrium is determined by an excess of reactants over the equilibrium amount. Once again, order on earth is generated at the expense of entropy increase of the sun. The total entropy of the earth and the rest of the universe increases, consistent with the Second Law.

生命化学系统也有类似的例子。太阳为绿色植物提供能量。绿色植物是其他生物化学系统的食物。被植物吸收并转化为化学能的能量在地球上产生了一个有序的、远离[化学平衡]的系统。在这里，与化学平衡的差异是由反应物超过平衡量所决定的。地球上的秩序再一次以太阳的熵增加为代价。地球和宇宙其他部分的总熵增加，符合第二定律

<math>{d \over dt}[ Y ] = k_2 [ X ] [Y ] - k_{3} [Y ] \,</math>.

[ y ] = k _ 2[ x ][ y ]-k _ {3}[ y ] ，[/math ].

Some autocatalytic reactions also generate order in a system at the expense of its surroundings. For example, ([[clock reactions]]) have [[reaction intermediate|intermediates]] whose concentrations oscillate in time, corresponding to temporal order. Other reactions generate spatial separation of [[chemical species]] corresponding to spatial order. More complex reactions are involved in [[metabolic pathway]]s and [[metabolic network]]s in [[biological systems]].
一些自催化反应也以牺牲周围环境为代价在系统中产生秩序。例如，（[[时钟反应]]）有[[反应中间体|中间体]]，其浓度随时间振荡，与时间顺序相对应。其他反应产生空间分离[[化学物种]]对应的空间顺序。在[[生物系统]]中的[[代谢途径]]s和[[代谢网络]]涉及更复杂的反应

Here, we have neglected the depletion of the reactant A, since its concentration is so large. The rate constants for the three reactions are <math>k_1</math>, <math>k_2</math>, and <math>k_3</math>, respectively.

在这里，我们忽略了反应物 a 的耗尽，因为它的浓度很大。这三个反应的速率常数分别是k1,k2,k3 。

The transition to order as the distance from equilibrium increases is not usually continuous. Order typically appears abruptly. The threshold between the disorder of chemical equilibrium and order is known as a [[phase transition]]. The conditions for a phase transition can be determined with the mathematical machinery of [[non-equilibrium thermodynamics]].

随着与平衡的距离增加，向有序的转变通常不是连续的。顺序通常会突然出现。化学平衡与有序之间的界限称为[[相变]]。相变的条件可以用[[非平衡态热力学]的数学机制来确定

This system of rate equations is known as the Lotka–Volterra equation and is most closely associated with population dynamics in predator–prey relationships. This system of equations can yield oscillating concentrations of the reaction intermediates X and Y. The amplitude of the oscillations depends on the concentration of A (which decreases without oscillation). Such oscillations are a form of emergent temporal order that is not present in equilibrium.

这个速率方程组被称为 Lotka-Volterra 方程，在捕食者-食饵关系中与族群动态最密切相关。这个方程组可以产生反应中间体 x 和 y 的振荡浓度。振荡的振幅取决于 a 的浓度(a 的浓度下降而没有振荡)。这种振荡是一种涌现的时间顺序，在平衡中不存在。

===Temporal order时间顺序===

A chemical reaction cannot oscillate about a position of final [[chemical equilibrium|equilibrium]] because the second law of thermodynamics requires that a [[thermodynamic system]] approach equilibrium and not recede from it. For a closed system at constant temperature and pressure, the [[Gibbs free energy]] must decrease continuously and not oscillate. However it is possible that the concentrations of some [[reaction intermediate]]s oscillate, and also that the ''rate'' of formation of products oscillates.<ref>Espenson, J.H. ''Chemical Kinetics and Reaction Mechanisms'' (2nd ed., McGraw-Hill 2002) p.190 {{ISBN|0-07-288362-6}}</ref>
一个化学反应不能围绕最终的[[化学平衡|平衡]]的位置振荡，因为热力学第二定律要求[[热力学系统]]接近平衡，而不是从中退却。对于一个恒温恒压的封闭系统，[[Gibbs自由能]必须连续下降而不振荡。然而，一些[[反应中间体]]的浓度可能会振荡，产物形成的“速率”也会振荡。

====Idealized example: Lotka–Volterra equation理想化例子：Lotka–Volterra 等式====

Another example of a system that demonstrates temporal order is the Brusselator (see Prigogine reference). It is characterized by the reactions

另一个演示时间顺序的系统例子是 Brusselator (见 Prigogine 参考文献)。人们的反应是拥有属性的

[[File:CentralTendencyLV.jpg|thumb|right|350px|The Lotka–Volterra equation is [[isomorphic]] with the predator–prey model and the two-reaction autocatalytic model. In this example baboons and cheetahs are equivalent to two different chemical species X and Y in autocatalytic reactions.]]

Consider a coupled set of two autocatalytic reactions in which the concentration of one of the reactants A is much larger than its equilibrium value. In this case, the forward reaction rate is so much larger than the reverse rates that we can neglect the reverse rates.
考虑一组耦合的两个自催化反应，其中一个反应物a的浓度远远大于其平衡值。在这种情况下，正向反应速率比反向速率大得多，我们可以忽略反向速率。
<math> A \rightarrow X</math>

《数学》 a right tarrow x

:<math> A + X \rightarrow 2X</math>

<math> 2X + Y \rightarrow 3X</math>

2X + y 右行3X

:<math> X + Y \rightarrow 2Y</math>

<math> B + X \rightarrow Y + D</math>

B + x 右边 y + d

:<math> Y \rightarrow E</math>

<math> X \rightarrow E</math>

X 右边的 e

with the rate equations

with the rate equations

用速率方程式

:<math>{d \over dt}[ X ] = k_1 [ A ] [X ] - k_{2} [X ][Y ] \,</math>

<math>{d \over dt}[ X ] = [A ] + [ X ]^2 [Y ] - [B ] [X ] - [X ] \,</math>

< math > { d over dt }[ x ] = [ a ] + [ x ] ^ 2[ y ]-[ b ][ x ]-[ x ] ，</math >

:<math>{d \over dt}[ Y ] = k_2 [ X ] [Y ] - k_{3} [Y ] \,</math>.

<math>{d \over dt}[ Y ] = [B ] [X ] - [ X ]^2 [Y ] \,</math>

[数学]{ d/dt }[ y ] = [ b ][ x ]-[ x ] ^ 2[ y ] ，[/math ]

Here, we have neglected the depletion of the reactant A, since its concentration is so large. The rate constants for the three reactions are <math>k_1</math>, <math>k_2</math>, and <math>k_3</math>, respectively.

where, for convenience, the rate constants have been set to 1.

为了方便起见，速率常数设置为1。

This system of rate equations is known as the [[Lotka–Volterra equation]] and is most closely associated with [[population dynamics]] in predator–prey relationships. This system of equations can yield oscillating concentrations of the reaction intermediates X and Y. The amplitude of the oscillations depends on the concentration of A (which decreases without oscillation). Such oscillations are a form of emergent temporal order that is not present in equilibrium.
这个速率方程组被称为[[Lotka–Volterra equation]]，在捕食者-猎物关系中与[[种群动力学]]联系最为密切。这个方程组可以得到反应中间体X和Y的振荡浓度，振荡的幅度取决于A的浓度（A的浓度减少而不振荡）。这种振荡是一种在平衡状态下不存在的突发时序形式。
The Brusselator in the unstable regime. A=1. B=2.5. X(0)=1. Y(0)=0. The system approaches a [[limit cycle. For B<1+A the system is stable and approaches a fixed point.]]

不稳定政权中的布鲁塞尔振子。 A=1. B=2.5. X(0)=1. Y(0)=0.该系统接近[极限环]。对于 b < 1 + a，系统是稳定的，并且接近一个固定点。]

The Brusselator has a fixed point at

布鲁塞尔振子有一个固定点

====Another idealized example: Brusselator另一个理想化模型：布鲁塞尔振子====

<math>[ X ] = A \,</math>

[数学] = a，[数学]

Another example of a system that demonstrates temporal order is the [[Brusselator]] (see Prigogine reference). It is characterized by the reactions

<math>[ Y ] = {B \over A} \,</math>.

[ math ][ y ] = { b over a } ，[ math ].

:<math> A \rightarrow X</math>

The fixed point becomes unstable when

定点变得不稳定，当

:<math> 2X + Y \rightarrow 3X</math>

<math> B>1+A^2 \,</math>

1 + a ^ 2,

:<math> B + X \rightarrow Y + D</math>

leading to an oscillation of the system. Unlike the Lotka-Volterra equation, the oscillations of the Brusselator do not depend on the amount of reactant present initially. Instead, after sufficient time, the oscillations approach a limit cycle.

导致了系统的振荡。与Lotka-Volterra 方程不同，布鲁塞尔振荡器的振荡并不取决于最初反应物的数量。相反，在足够的时间之后，振荡接近极限环。

:<math> X \rightarrow E</math>

with the rate equations

An idealized example of spatial spontaneous symmetry breaking is the case in which we have two boxes of material separated by a permeable membrane so that material can diffuse between the two boxes. It is assumed that identical Brusselators are in each box with nearly identical initial conditions. (see Prigogine reference)

一个理想化的空间自发对称性破缺的例子是，我们有两个盒子的材料被一个可渗透的薄膜分开，这样材料可以在两个盒子之间扩散。我们假设在每个盒子中都有相同的布鲁塞尔振子，并且具有几乎相同的初始条件。(见 Prigogine 参考文献)

:<math>{d \over dt}[ X ] = [A ] + [ X ]^2 [Y ] - [B ] [X ] - [X ] \,</math>

<math>{d \over dt}[ X_1 ] = [A ] + [ X _1]^2 [Y_1 ] - [B ] [X_1 ] - [X_1 ] + D_x\left( X_2 - X_1 \right)\,</math>

< math > { d over dt }[ x _ 1] = [ a ] + [ x _ 1] ^ 2[ y _ 1]-[ b ][ x _ 1]-[ x _ 1] + d _ x 左(x _ 2-x _ 1右) ，</math >

:<math>{d \over dt}[ Y ] = [B ] [X ] - [ X ]^2 [Y ] \,</math>

<math>{d \over dt}[ Y_1 ] = [B ] [X_1 ] - [ X_1 ]^2 [Y_1 ] + D_y\left( Y_2 - Y_1\right) \,</math>

< math > { d over dt }[ y _ 1] = [ b ][ x _ 1]-[ x _ 1] ^ 2[ y _ 1] + d _ y 左(y _ 2-y _ 1右) ，</math >

where, for convenience, the rate constants have been set to 1.
其中，为了方便起见，速率常数被设置为1。
<math>{d \over dt}[ X_2 ] = [A ] + [ X _2]^2 [Y_2 ] - [B ] [X_2 ] - [X_2 ] + D_x\left( X_1 - X_2 \right)\,</math>

[ x _ 2] = [ a ] + [ x _ 2] ^ 2[ y _ 2]-[ b ][ x _ 2]-[ x _ 2] + d _ x 左(x _ 1-x _ 2右) ，</math >

[[File:080205 Brusselator picture.jpg|thumb|right|350px|The Brusselator in the unstable regime. A=1. B=2.5. X(0)=1. Y(0)=0. The system approaches a [[limit cycle]]. For B<1+A the system is stable and approaches a [[Fixed point (mathematics)|fixed point]].]]

<math>{d \over dt}[ Y_2 ] = [B ] [X_2 ] - [ X_2 ]^2 [Y_2 ] + D_y\left( Y_1 - Y_2\right) \,</math>

[ math ]{ d over dt }[ y _ 2] = [ b ][ x _ 2]-[ x _ 2] ^ 2[ y _ 2] + d _ y 左(y _ 1-y _ 2右) ，</math >

The Brusselator has a fixed point at
布鲁塞尔振子有一个固定点在

Here, the numerical subscripts indicate which box the material is in. There are additional terms proportional to the diffusion coefficient D that account for the exchange of material between boxes.

在这里，数字下标表示材料在哪个盒子里。还有一些与扩散系数 d 成比例的附加项，用于解释盒子之间的物质交换。

:<math>[ X ] = A \,</math>

If the system is initiated with the same conditions in each box, then a small fluctuation will lead to separation of materials between the two boxes. One box will have a predominance of X, and the other will have a predominance of Y.

如果系统启动时每个盒子的条件相同，那么一个小的波动将导致两个盒子之间的物料分离。一个盒子将具有 x 的优势，而另一个盒子将具有 y 的优势。

:<math>[ Y ] = {B \over A} \,</math>.

The fixed point becomes unstable when

固定点变得不稳定当

Real examples of clock reactions are the Belousov–Zhabotinsky reaction (BZ reaction), the Briggs–Rauscher reaction, the Bray–Liebhafsky reaction and the iodine clock reaction. These are oscillatory reactions, and the concentration of products and reactants can be approximated in terms of damped oscillations.

时钟反应的真实例子是 Belousov-Zhabotinsky 反应(BZ 反应) ，Briggs-Rauscher 反应，Bray-Liebhafsky 反应和碘钟反应。这些都是振荡反应，产物和反应物的浓度可以用阻尼振荡来近似。

:<math> B>1+A^2 \,</math>

The best-known reaction, the BZ reaction, can be created with a mixture of potassium bromate <chem>(KBrO3)</chem>, malonic acid <chem>(CH2(COOH)2)</chem>, and manganese sulfate <chem>(MnSO4)</chem> prepared in a heated solution with sulfuric acid <chem>(H2SO4)</chem> as solvent.

其中最著名的反应是 BZ 反应，它是在硫酸 </chem > (H2SO4) </chem > (H2SO4) </chem > (CH2(COOH)2) </chem > 和用硫酸 </chem > (MnSO4) </chem > 加热溶液中制得的混合溴酸钾。

leading to an oscillation of the system. Unlike the Lotka-Volterra equation, the oscillations of the Brusselator do not depend on the amount of reactant present initially. Instead, after sufficient time, the oscillations approach a [[limit cycle]].<ref>{{cite web

|url=http://www.math.ohio-state.edu/~ault/Papers/Brusselator.pdf

|title=Archived copy

Another autocatalytic system is one driven by light coupled to photo-polymerization reactions. In a process termed optical autocatalysis, positive feedback is created between light intensity and photo-polymerization rate, via polymerization-induced increases in the refractive index. Light's preference to occupy regions of higher refractive index results in leakage of light into regions of higher molecular weight, thereby amplifying the photo-chemical reaction. The positive feedback may be expressed as:

另一种自催化体系是由光与光聚合反应耦合驱动的体系。在一个被称为光学自催化的过程中，光强度和光聚合速率之间产生正反馈，通过聚合诱导增加折射率。光喜欢占据折射率较高的区域，导致光线泄漏到分子量较高的区域，从而放大了光化学反应。积极的反馈可以表示为:

|accessdate=2015-10-15

|url-status=dead

<math>\text{polymerization rate} \to \text{molecular weight}/\text{refractive index} \to \text{intensity}</math>

文本{分子量}/文本{折射率}到文本{密度}

|archiveurl=https://web.archive.org/web/20081217020941/http://www.math.ohio-state.edu/~ault/Papers/Brusselator.pdf

|archivedate=2008-12-17

Noting that photo-polymerization rate is proportional to intensity and that refractive index is proportional to molecular weight, the positive feedback between intensity and photo-polymerization establishes the auto-catalytic behavior. Optical auto-catalysis has been shown to result on spontaneous pattern formation in photopolymers. Hosein and co-workers discovered that optical autocatalysis can also occur in photoreactive polymer blends, and that the process can induce binary phase morphologies with the same pattern as the light profile. Glycolysis consists of the degradation of one molecule of glucose and the overall production of two molecules of ATP. The process is therefore of great importance to the energetics of living cells. The global glycolysis reaction involves glucose, ADP, NAD, pyruvate, ATP, and NADH.

注意到光聚合速率与强度成正比，折射率与分子量成正比，强度与光聚合之间的正反馈建立了自催化行为。光学自催化已被证明是光聚合物自发形成图案的原因。Hosein和他的合作者发现，光学自催化也可以发生在光反应聚合物共混物中，这一过程可以诱导形成与光型相同的二元相形态。糖酵解是由一个葡萄糖分子的降解和两个 ATP 分子的全部产生组成。因此，这个过程对活细胞的能量学来说是非常重要的。糖酵解反应包括葡萄糖、 ADP、 NAD、丙酮酸、 ATP 和 NADH。

}} Dynamics of the Brusselator

</ref>

<chem>glucose{} + 2ADP{} + 2P_\mathit{i}{} + 2NAD -> 2(pyruvate){} + 2ATP{} + 2NADH</chem>.

< chem > glucose {} + 2ADP {} + 2P _ mathit { i }{} + 2NAD-> 2(丙酮酸盐){} + 2ATP {} + 2NADH </chem > 。

===Spatial order空间秩序===

The details of the process are quite involved, however, a section of the process is autocatalyzed by phosphofructokinase (PFK). This portion of the process is responsible for oscillations in the pathway that lead to the process oscillating between an active and an inactive form. Thus, the autocatalytic reaction can modulate the process.

该过程的细节相当复杂，然而，该过程的一部分是由磷酸果糖激酶(PFK)自催化的。这部分的过程负责振荡的路径，导致过程之间的振荡活跃和非活跃的形式。因此，自催化反应可以调节这一过程。

An idealized example of spatial [[spontaneous symmetry breaking]] is the case in which we have two boxes of material separated by a permeable membrane so that material can [[diffusion|diffuse]] between the two boxes. It is assumed that identical Brusselators are in each box with nearly identical initial conditions. (see Prigogine reference)

:<math>{d \over dt}[ X_1 ] = [A ] + [ X _1]^2 [Y_1 ] - [B ] [X_1 ] - [X_1 ] + D_x\left( X_2 - X_1 \right)\,</math>

It is possible to use the results from an autocatalytic reaction coupled with reaction–diffusion system theory to tailor the design of a thin layer. The autocatalytic process allows controlling the nonlinear behavior of the oxidation front, which is used to establish the initial geometry needed to generate the arbitrary final geometry. It has been successfully done in the wet oxidation of <math>Al_xGa_{1-x}As</math> to obtain arbitrary shaped layers of <math>AlO_x</math>.

利用自催化反应结合反应扩散系统理论的结果来设计薄层是可能的。自催化过程允许控制氧化前沿的非线性行为，用于建立生成任意最终几何所需的初始几何。在湿式氧化法中，成功地获得了任意形状的氧化铝层。

:<math>{d \over dt}[ Y_1 ] = [B ] [X_1 ] - [ X_1 ]^2 [Y_1 ] + D_y\left( Y_2 - Y_1\right) \,</math>

:<math>{d \over dt}[ X_2 ] = [A ] + [ X _2]^2 [Y_2 ] - [B ] [X_2 ] - [X_2 ] + D_x\left( X_1 - X_2 \right)\,</math>

The initial amounts of reactants determine the distance from a chemical equilibrium of the system. The greater the initial concentrations the further the system is from equilibrium. As the initial concentration increases, an abrupt change in order occurs. This abrupt change is known as phase transition. At the phase transition, fluctuations in macroscopic quantities, such as chemical concentrations, increase as the system oscillates between the more ordered state (lower entropy, such as ice) and the more disordered state (higher entropy, such as liquid water). Also, at the phase transition, macroscopic equations, such as the rate equations, fail. Rate equations can be derived from microscopic considerations. The derivations typically rely on a mean field theory approximation to microscopic dynamical equations. Mean field theory breaks down in the presence of large fluctuations (see Mean field theory article for a discussion). Therefore, since large fluctuations occur in the neighborhood of a phase transition, macroscopic equations, such as rate equations, fail. As the initial concentration increases further, the system settles into an ordered state in which fluctuations are again small. (see Prigogine reference)

反应物的初始量决定了与体系化学平衡的距离。初始浓度越大，系统离平衡越远。随着初始浓度的增加，顺序发生突变。这种突变被称为相变。在相变阶段，宏观量的波动，如化学浓度，随着系统在更有序的状态（低熵，如冰）和更无序的状态（更高的熵，如液态水）之间振荡而增加。同样，在相变过程中，宏观方程，如速率方程，会失效。速率方程可以从微观角度推导出来。推导通常依赖于对微观动力学方程的平均场理论近似。平均场理论在大波动的存在下会崩溃（见平均场理论文章的讨论）。因此，由于大的波动发生在相变附近，例如速率方程等的宏观方程便失灵了。随着初始浓度的进一步增加，系统进入有序状态，在这种状态下波动又很小(见 Prigogine 参考文献)

:<math>{d \over dt}[ Y_2 ] = [B ] [X_2 ] - [ X_2 ]^2 [Y_2 ] + D_y\left( Y_1 - Y_2\right) \,</math>

Here, the numerical subscripts indicate which box the material is in. There are additional terms proportional to the diffusion coefficient D that account for the exchange of material between boxes.

在这里，数字下标表示材料在哪个盒子里。还有一些与扩散系数D成比例的附加项，它们解释了盒子之间的物质交换。

Asymmetric autocatalysis occurs when the reaction product is chiral and thus acts as a chiral catalyst for its own production. Reactions of this type, such as the Soai reaction, have the property that they can amplify a very small enantiomeric excess into a large one. This has been proposed as an important step in the origin of biological homochirality.

不对称自催化反应发生在反应产物是手性的情况下，因此可以作为手性催化剂自身生产。这种类型的反应，比如 Soai 反应，具有将非常小的对映体过量百分数放大成大的反应的特性。这被认为是生物同手性起源的重要步骤。

If the system is initiated with the same conditions in each box, then a small fluctuation will lead to separation of materials between the two boxes. One box will have a predominance of X, and the other will have a predominance of Y.
如果系统在每个箱子的相同条件下启动，那么小的波动将导致两个箱子之间的物料分离。一个方框的优势是X，另一个方框的优势是Y。

==Real examples实例==

Real examples of [[clock reaction]]s are the [[Belousov–Zhabotinsky reaction]] (BZ reaction), the [[Briggs–Rauscher reaction]], the [[Bray–Liebhafsky reaction]] and the [[iodine clock reaction]]. These are oscillatory reactions, and the concentration of products and reactants can be approximated in terms of [[damping|damped]] [[oscillation]]s.
时钟反应]]的真正例子是[[Belousov–Zhabotinsky reaction]]（BZ反应）、[[Briggs–Rauscher 反应]]、[[Bray–Liebhafsky 反应]]和[[碘钟反应]]。这些都是振荡反应，产物和反应物的浓度可以用阻尼，振荡来近似。
In 1995 Stuart Kauffman proposed that life initially arose as autocatalytic chemical networks.

1995年，Stuart Kauffman提出生命最初是以自催化化学网络的形式出现的。

The best-known reaction, the BZ reaction, can be created with a mixture of potassium bromate <chem>(KBrO3)</chem>, malonic acid <chem>(CH2(COOH)2)</chem>, and manganese sulfate <chem>(MnSO4)</chem> prepared in a heated solution with sulfuric acid <chem>(H2SO4)</chem> as solvent.<ref>{{Cite web|url=http://online.redwoods.cc.ca.us/instruct/darnold/deproj/Sp98/Gabe/|title=The Belousov-Zhabotinsky Reaction|last=Peterson|first=Gabriel|date=|website=|accessdate=|archiveurl=https://web.archive.org/web/20121231011212/http://online.redwoods.cc.ca.us/instruct/darnold/deproj/Sp98/Gabe/|archivedate=December 31, 2012}}</ref>

British ethologist Richard Dawkins wrote about autocatalysis as a potential explanation for abiogenesis in his 2004 book The Ancestor's Tale. He cites experiments performed by Julius Rebek and his colleagues at the Scripps Research Institute in California in which they combined amino adenosine and pentafluorophenyl ester with the autocatalyst amino adenosine triacid ester (AATE). One system from the experiment contained variants of AATE which catalyzed the synthesis of themselves. This experiment demonstrated the possibility that autocatalysts could exhibit competition within a population of entities with heredity, which could be interpreted as a rudimentary form of natural selection, and that certain environmental changes (such as irradiation) could alter the chemical structure of some of these self-replicating molecules (an analog for mutation) in such ways that could either boost or interfere with its ability to react, thus boosting or interfering with its ability to replicate and spread in the population.

英国动物行为学家 Richard Dawkins在他2004年出版的《祖先的故事》一书中提到了自我催化作为自然发生的潜在解释。他引用了 Julius Rebek 和他的同事们在加利福尼亚斯克里普斯研究所进行的实验，他们将氨基腺苷和五氟苯酯与氨基腺苷三酸酯(AATE)结合在一起。实验中的一个系统包含了催化自身合成的 AATE 的变体。这项实验证明了这样一种可能性，即自动催化剂可以在具有遗传性的实体群体中展现竞争，这可以被解释为一种基本的自然选择形式，而且某些环境变化(如辐照)可以改变某些自我复制分子(变异的类似物)的化学结构，这种方式可以增强或干扰其反应能力，从而增强或干扰其复制和在群体中传播的能力。

== Optics example光学实例 ==

Autocatalysis plays a major role in the processes of life. Two researchers who have emphasized its role in the origins of life are Robert Ulanowicz and Stuart Kauffman.

自动催化在生命过程中起着重要的作用。强调其在生命起源中的作用的两位研究人员是Robert Ulanowicz和Stuart Kauffman。

Another autocatalytic system is one driven by light coupled to photo-polymerization reactions. In a process termed optical autocatalysis, positive feedback is created between light intensity and photo-polymerization rate, via polymerization-induced increases in the refractive index. Light's preference to occupy regions of higher refractive index results in leakage of light into regions of higher molecular weight, thereby amplifying the photo-chemical reaction. The positive feedback may be expressed as:<ref name=":0">{{Cite journal|last=Biria|first=Saeid|last2=Malley|first2=Phillip P. A.|last3=Kahan|first3=Tara F.|last4=Hosein|first4=Ian D.|date=2016-11-15|title=Optical Autocatalysis Establishes Novel Spatial Dynamics in Phase Separation of Polymer Blends during Photocuring|journal=ACS Macro Letters|volume=5|issue=11|pages=1237–1241|doi=10.1021/acsmacrolett.6b00659}}</ref>

Autocatalysis occurs in the initial transcripts of rRNA. The introns are capable of excising themselves by the process of two nucleophilic transesterification reactions. The RNA able to do this is sometimes referred to as a ribozyme. Additionally, the citric acid cycle is an autocatalytic cycle run in reverse.

自我催化发生在RNA的最初转录本中。这些内含子能够通过两个亲核酯交换反应反应自我激活。能够做到这一点的 RNA 有时被称为核酶。此外，三羧酸循环是一种反向运行的自动催化循环。

:<math>\text{polymerization rate} \to \text{molecular weight}/\text{refractive index} \to \text{intensity}</math>

Ultimately, biological metabolism itself can be seen as a vast autocatalytic set, in that all of the molecular constituents of a biological cell are produced by reactions involving this same set of molecules.

最终，生物的新陈代谢本身可以被看作是一个巨大的自我催化装置，因为一个生物细胞的所有分子成分都是由包含同一组分子的反应产生的。

Noting that photo-polymerization rate is proportional to intensity<ref>{{Cite journal|last=Decker|first=Christian|date=1998-02-01|title=The use of UV irradiation in polymerization|url=|journal=Polymer International|language=en|volume=45|issue=2|pages=133–141 |doi=10.1002/(SICI)1097-0126(199802)45:2<133::AID-PI969>3.0.CO;2-F}}</ref> and that refractive index is proportional to molecular weight,<ref>{{Cite journal|last=Askadskii|first=A. A.|year=1990|title=Influence of crosslinking density on the properties of polymer networks|journal=Polymer Science U.S.S.R.|volume=32|issue=10|pages=2061–2069|doi=10.1016/0032-3950(90)90361-9}}</ref> the positive feedback between intensity and photo-polymerization establishes the auto-catalytic behavior. Optical auto-catalysis has been shown to result on spontaneous [[pattern formation]] in photopolymers.<ref>{{Cite journal|last=Burgess|first=Ian B.|last2=Shimmell|first2=Whitney E.|last3=Saravanamuttu|first3=Kalaichelvi|date=2007-04-01|title=Spontaneous Pattern Formation Due to Modulation Instability of Incoherent White Light in a Photopolymerizable Medium|journal=Journal of the American Chemical Society|volume=129|issue=15|pages=4738–4746|doi=10.1021/ja068967b|pmid=17378567|issn=0002-7863}}</ref><ref>{{Cite journal|last=Basker|first=Dinesh K.|last2=Brook|first2=Michael A.|last3=Saravanamuttu|first3=Kalaichelvi|title=Spontaneous Emergence of Nonlinear Light Waves and Self-Inscribed Waveguide Microstructure during the Cationic Polymerization of Epoxides|journal=The Journal of Physical Chemistry C|language=en|volume=119|issue=35|pages=20606–20617|doi=10.1021/acs.jpcc.5b07117|year=2015}}</ref><ref>{{Cite journal|last=Biria|first=Saeid|last2=Malley|first2=Philip P. A.|last3=Kahan|first3=Tara F.|last4=Hosein|first4=Ian D.|date=2016-03-03|title=Tunable Nonlinear Optical Pattern Formation and Microstructure in Cross-Linking Acrylate Systems during Free-Radical Polymerization|journal=The Journal of Physical Chemistry C|volume=120|issue=8|pages=4517–4528|doi=10.1021/acs.jpcc.5b11377|issn=1932-7447}}</ref> Hosein and co-workers discovered that optical autocatalysis can also occur in photoreactive polymer blends, and that the process can induce binary phase morphologies with the same pattern as the light profile.<ref name=":0" /> The light undergoes optical [[Modulational instability|modulation instability]], spontaneous dividing into a multitude of optical filaments, and the polymer system thereby forms filaments within the blend structure.<ref name=":0" /> The result is a new system that couples optical autocatalytic behavior to [[spinodal decomposition]].
注意到光聚合速率与强度成正比，折射率与分子量成正比，强度和光聚合之间的正反馈建立了自催化行为。光自催化已经被证明可以导致光聚合物中自发图案的形成。Hosein和他的同事发现，光自催化也可以发生在光活性聚合物混合物中，并且该过程可以诱导具有与光轮廓相同图案的二元相形态。光经历了光调制不稳定性，自发地分裂成许多光学细丝，因此，聚合物系统在共混结构中形成细丝。结果是一个将光学自催化行为与旋节分解相耦合的新系统。

==Biological example生物实例==

It is known that an important metabolic cycle, [[glycolysis]], displays temporal order.<ref>{{cite book | author=G. Nicolis and [[Ilya Prigogine]] | title=Self-Organization in Nonequilibrium Systems | location= New York | publisher=John Wiley and Sons| year=1977 | isbn=978-0-471-02401-9}}

</ref> Glycolysis consists of the degradation of one molecule of glucose and the overall production of two molecules of [[Adenosine triphosphate|ATP]]. The process is therefore of great importance to the energetics of living cells. The global glycolysis reaction involves [[glucose]], [[Adenosine diphosphate|ADP]], [[Nicotinamide adenine dinucleotide|NAD]], [[Pyruvic acid|pyruvate]], [[Adenosine triphosphate|ATP]], and NADH.
糖酵解包括一个葡萄糖分子的降解和两个分子[[三磷酸腺苷| ATP]]的合成。因此，这个过程对活细胞的能量学非常重要。全局糖酵解反应涉及[[葡萄糖]]、[[二磷酸腺苷| ADP]]、[[烟酰胺腺嘌呤二核苷酸| NAD]]

:<chem>glucose{} + 2ADP{} + 2P_\mathit{i}{} + 2NAD -> 2(pyruvate){} + 2ATP{} + 2NADH</chem>.

The details of the process are quite involved, however, a section of the process is autocatalyzed by [[phosphofructokinase]] (PFK). This portion of the process is responsible for oscillations in the pathway that lead to the process oscillating between an active and an inactive form. Thus, the autocatalytic reaction can modulate the process.

过程的细节是相当复杂的，然而，过程的一部分是由[[磷酸果糖激酶]]（PFK）自动催化的。这个过程的这一部分负责路径中的振荡，导致过程在一个活跃的和一个不活跃的形式之间振荡。因此，自催化反应可以调节这一过程。

==Shape tailoring of thin layers薄层剪裁==

It is possible to use the results from an autocatalytic reaction coupled with [[reaction–diffusion system]] theory to tailor the design of a thin layer. The autocatalytic process allows controlling the nonlinear behavior of the oxidation [[Front (physics)|front]], which is used to establish the initial geometry needed to generate the arbitrary final geometry.<ref>{{cite journal |last1=Alfaro-Bittner |first1=K. |last2=Rojas |first2=R.G. |last3=Lafleur |first3=G. |last4=Calvez |first4=S. |last5=Almuneau |first5=G. |last6=Clerc |first6=M.G. |last7=Barbay |first7=S. |title=Modeling the Lateral Wet Oxidation of into Arbitrary Mesa Geometries |journal=Physical Review Applied|date=22 April 2019|volume=11 |issue=4|page=044067|doi=10.1103/PhysRevApplied.11.044067|url=https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.11.044067}}</ref> It has been successfully done in the wet oxidation of <math>Al_xGa_{1-x}As</math> to obtain arbitrary shaped layers of <math>AlO_x</math>.
利用自催化反应与[[反应-扩散系统]]理论相结合的结果，可以定制薄层的设计。自动催化过程允许控制氧化的非线性行为，用于建立生成任意最终几何体所需的初始几何体

==Phase transitions相变==

The initial amounts of reactants determine the distance from a chemical equilibrium of the system. The greater the initial concentrations the further the system is from equilibrium. As the initial concentration increases, an abrupt change in [[entropy|order]] occurs. This abrupt change is known as [[phase transition]]. At the phase transition, fluctuations in macroscopic quantities, such as chemical concentrations, increase as the system oscillates between the more ordered state (lower entropy, such as ice) and the more disordered state (higher entropy, such as liquid water). Also, at the phase transition, macroscopic equations, such as the rate equations, fail. Rate equations can be derived from microscopic considerations. The derivations typically rely on a [[mean field theory]] approximation to microscopic dynamical equations. Mean field theory breaks down in the presence of large fluctuations (see [[Mean field theory]] article for a discussion). Therefore, since large fluctuations occur in the neighborhood of a phase transition, macroscopic equations, such as rate equations, fail. As the initial concentration increases further, the system settles into an ordered state in which fluctuations are again small. (see Prigogine reference)

反应物的初始量决定了与体系化学平衡的距离。初始浓度越大，系统离平衡越远。随着初始浓度的增加，[[熵|阶]]发生突变。这种突变被称为[[相变]]。在相变阶段，宏观量的波动，如化学浓度，随着系统在更有序的状态（低熵，如冰）和更无序的状态（更高的熵，如液态水）之间振荡而增加。同样，在相变过程中，宏观方程，如速率方程，会失效。速率方程可以从微观角度推导出来。推导通常依赖于对微观动力学方程的[[平均场理论]]近似。平均场理论在大波动的情况下会崩溃（见[[平均场理论]]文章进行讨论）。因此，由于大的波动发生在相变附近，宏观方程，如速率方程，失败了。随着初始浓度的进一步增加，系统进入有序状态，在这种状态下波动又很小。（见Prigogine参考文献）

==Asymmetric autocatalysis不对称自催化 ==

Asymmetric autocatalysis occurs when the reaction product is [[chiral]] and thus acts as a chiral catalyst for its own production. Reactions of this type, such as the [[Soai reaction]], have the property that they can amplify a very small [[enantiomeric excess]] into a large one. This has been proposed as an important step in the origin of biological [[homochirality]].<ref name="Soai2001">{{cite journal|vauthors=Soai K, Sato I, Shibata T | title=Asymmetric autocatalysis and the origin of chiral homogeneity in organic compounds. | journal=The Chemical Record | year= 2001 | volume= 1 | issue= 4 | pages= 321–32 | pmid=11893072 | doi= 10.1002/tcr.1017| pmc= }}</ref>
非对称自催化发生在反应产物为[[手性]]时，因此作为手性催化剂进行自身生产。这种类型的反应，如[[Soai反应]]，具有将很小的[[对映体过量]]放大为大反应的性质。在这一点上，手性被认为是生物起源的一个重要步骤

== Role in origin of life生命起源中的角色 ==

{{main|Abiogenesis}}

In 1995 [[Stuart Kauffman]] proposed that life initially arose as autocatalytic chemical networks.<ref>{{cite book|author=Stuart Kauffman|title=At Home in the Universe: The Search for the Laws of Self-Organization and Complexity|isbn=978-0-19-509599-9|publisher=Oxford University Press|year=1995|url-access=registration|url=https://archive.org/details/athomeinuniverse00kauf_0}}</ref>
1995年[[Stuart Kauffman]]提出生命最初是以自催化化学网络的形式出现的

Category:Catalysis

类别: 催化

<noinclude>

This page was moved from [[wikipedia:en:Autocatalysis]]. Its edit history can be viewed at [[自催化/edithistory]]</noinclude>

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