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'''.
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'''。<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.</ref>这种反应称为'''自催化反应 autocatalytic reaction'''。
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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 chemical reaction of two reactants and two products can be written as
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两种反应物和两种产物的化学反应可以写成
两种反应物和两种产物的化学反应可以写成
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:<math> \alpha A + \beta B \rightleftharpoons \sigma S + \tau T</math>
:<math> \alpha A + \beta B \rightleftharpoons \sigma S + \tau T</math>
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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.
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.
Here, the brackets indicate the concentration of the chemical species, in [[mole (unit)|moles]] per liter, and k<sub>+</sub> and k<sub>−</sub> are [[rate constant]]s.
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
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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
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:<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>
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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（当每个物种<math>{d \over dt}=0</math>）。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。<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>
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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>
[[文件:Sigmoid curve for an autocatalytical reaction.jpg|链接=link=Special:FilePath/Sigmoid_curve_for_an_autocatalytical_reaction.jpg|替代=|缩略图|Sigmoid variation of product concentration in autocatalytic reactions]]
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[[文件:Sigmoid curve for an autocatalytical reaction.jpg|自催化反应中产物浓度的 s 形变化]]
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Sigmoid variation of product concentration in autocatalytic reactions
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自催化反应中产物浓度的 s 形变化
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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/>
:<math>{d \over dt}[ A ] =- k_+ [ A ] [B ] + k_{-} [B ]^2 \,</math>
:<math>{d \over dt}[ A ] =- k_+ [ A ] [B ] + k_{-} [B ]^2 \,</math>
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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.
:<math>{d \over dt}[ B ] = + k_+ [ A ] [B ] -k_{-} [B ]^2 \,</math>.
:<math>{d \over dt}[ B ] = + k_+ [ A ] [B ] -k_{-} [B ]^2 \,</math>.
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使用速率方程（对于基本反应）
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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.
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.
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.
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.
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.
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>
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.
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.
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.
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/>
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.]]
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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
==秩序创立==
==秩序创立==
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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.
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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。
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]].
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.
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 }}
</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.
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 <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 }}</ref> 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。
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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.
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]].
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 。
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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]].
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.
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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。
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>
[[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.|链接=Special:FilePath/CentralTendencyLV.jpg]]
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.
:<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>
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:<math>{d \over dt}[ Y ] = k_2 [ X ] [Y ] - k_{3} [Y ] \,</math>.
:<math>{d \over dt}[ Y ] = k_2 [ X ] [Y ] - k_{3} [Y ] \,</math>.
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Here, we have neglected the depletion of the reactant A, since its concentration is so large. The rate constants for the three reactions are
这里，我们忽略了反应物A的消耗，因为它的浓度很大。这三个反应的速率常数是
这里，我们忽略了反应物A的消耗，因为它的浓度很大。这三个反应的速率常数是
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<math>k_1</math>, <math>k_2</math>, and <math>k_3</math>, respectively.
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<math>k_1</math>, <math>k_2</math>, and <math>k_3</math>.
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where, for convenience, the rate constants have been set to 1.
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为了方便起见，速率常数设置为1。
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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.
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.]]
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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。]
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The Brusselator has a fixed point at
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这个速率方程组被称为[[Lotka–Volterra方程式]]，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。
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布鲁塞尔振子有一个固定点
====另一个理想化模型：布鲁塞尔振子 ====
====另一个理想化模型：布鲁塞尔振子 ====
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Another example of a system that demonstrates temporal order is the [[Brusselator]] (see Prigogine reference). It is characterized by the reactions
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)
[[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]].|链接=Special:FilePath/080205_Brusselator_picture.jpg]]
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.
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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>
:<math>[ X ] = A \,</math>
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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.
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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。
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:<math>[ Y ] = {B \over A} \,</math>.
:<math>[ Y ] = {B \over A} \,</math>.
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The fixed point becomes unstable when
固定点变得不稳定当
固定点变得不稳定当
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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.
导致系统振荡。与 Lotka-Volterra 方程不同，Brusselator 的振荡不取决于最初存在的反应物的量。相反，在足够的时间之后，振荡接近极限循环。<ref>{{cite web |url=http://www.math.ohio-state.edu/~ault/Papers/Brusselator.pdf |title=Archived copy |accessdate=2015-10-15 |url-status=dead
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|archiveurl=https://web.archive.org/web/20081217020941/http://www.math.ohio-state.edu/~ault/Papers/Brusselator.pdf |archivedate=2008-12-17 }} Dynamics of the Brusselator
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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.
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
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:
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.
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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。
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.
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)
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>.
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)
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.
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.
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.
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.
In 1995 Stuart Kauffman proposed that life initially arose as autocatalytic chemical networks.
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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。
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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>
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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.
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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。
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== 光学实例 ==
== 光学实例 ==
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另一种自催化系统是由光耦合到光聚合反应驱动的。在一个称为光自催化的过程中，通过聚合引起的折射率增加，光强度和光聚合速率之间产生了正反馈。光倾向于占据高折射率区域，从而导致光泄漏到高分子量区域，从而放大了光化学反应。正反馈可以表示为:<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>
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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.
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.
注意到光聚合速率与强度成正比，<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>折射率与分子量成正比，<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>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。<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。<ref name=":0" /> 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。<ref name=":0" /> 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。
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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.
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]].
众所周知，一个重要的代谢循环，即糖酵解，显示出时间顺序。<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> 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]]、丙酮酸、 [[三磷酸腺苷|ATP]] 和 [[NADH]]。
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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}}
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</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.
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.
可以使用自催化反应的结果与反应-扩散系统理论相结合来定制薄层的设计。自催化过程允许控制氧化前沿的非线性行为，该行为用于建立生成任意最终几何形状所需的初始几何形状。[<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>已在湿法氧化中成功完成<math>Al_xGa_{1-x}As</math>获得任意形状的层<math>AlO_x</math>。
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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>.
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)
<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>
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== 生命起源中的角色 ==
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1995 年[[斯图尔特·艾伦·考夫曼 Stuart Alan Kauffman]]提出生命最初是作为自催化化学网络出现的。<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>
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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>
英国 动物行为学家理查德·道金斯 Richard Dawkins在他 2004 年出版的《祖先的故事 The Ancestor's Tale》一书中将自催化作为对非生物发生的潜在解释。他引用了加利福尼亚斯克里普斯研究所的 Julius Rebek 和他的同事进行的实验，他们将氨基腺苷和五氟苯酯与自催化剂氨基腺苷三酸酯 (AATE) 结合在一起。实验中的一个系统包含催化自身合成的 AATE 变体。该实验证明了自动催化剂可能在具有遗传的实体群体中表现出竞争的可能性，这可以解释为一种基本形式自然选择，并且某些环境变化（例如辐照）可能会改变其中一些自我复制分子（突变的类似物）的化学结构，从而增强或干扰其反应能力，从而增强或干扰其反应能力。干扰其在人群中复制和传播的能力。<ref>Rebeck, Julius (July 1994). "Synthetic Self-Replicating Molecules". Scientific American: 48–55.</ref>
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== 生命起源中的角色 ==
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自催化在生命过程中发挥着重要作用。两位强调其在生命起源中的作用的研究人员是 Robert Ulanowicz <ref>Ecology, the Ascendent Perspective", Robert Ulanowicz, Columbia Univ. Press 1997.</ref>和 Stuart Kauffman。<ref>Investigations, Stuart Kauffman.</ref>
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>
↑Steinfeld J.I., Francisco J.S. and Hase W.L. Chemical Kinetics and Dynamics (2nd ed., Prentice-Hall 1999) p.151-2.
↑Ross, John; Garcia-Colin, Leopoldo S. (March 1989). "Thermodynamics of chemical systems far from equilibrium". The Journal of Physical Chemistry. 93 (5): 2091–2092. doi:10.1021/j100342a075.
↑Espenson, J.H. Chemical Kinetics and Reaction Mechanisms (2nd ed., McGraw-Hill 2002) p.190.
↑"Archived copy"(PDF). Archived from the original(PDF) on 2008-12-17. Retrieved 2015-10-15.{{cite web}}: CS1 maint: archived copy as title (link) Dynamics of the Brusselator
↑Askadskii, A. A. (1990). "Influence of crosslinking density on the properties of polymer networks". Polymer Science U.S.S.R. 32 (10): 2061–2069. doi:10.1016/0032-3950(90)90361-9.
↑Burgess, Ian B.; Shimmell, Whitney E.; Saravanamuttu, Kalaichelvi (2007-04-01). "Spontaneous Pattern Formation Due to Modulation Instability of Incoherent White Light in a Photopolymerizable Medium". Journal of the American Chemical Society. 129 (15): 4738–4746. doi:10.1021/ja068967b. ISSN0002-7863. PMID17378567.
↑Basker, Dinesh K.; Brook, Michael A.; Saravanamuttu, Kalaichelvi (2015). "Spontaneous Emergence of Nonlinear Light Waves and Self-Inscribed Waveguide Microstructure during the Cationic Polymerization of Epoxides". The Journal of Physical Chemistry C (in English). 119 (35): 20606–20617. doi:10.1021/acs.jpcc.5b07117.
↑Biria, Saeid; Malley, Philip P. A.; Kahan, Tara F.; Hosein, Ian D. (2016-03-03). "Tunable Nonlinear Optical Pattern Formation and Microstructure in Cross-Linking Acrylate Systems during Free-Radical Polymerization". The Journal of Physical Chemistry C. 120 (8): 4517–4528. doi:10.1021/acs.jpcc.5b11377. ISSN1932-7447.
↑Soai K, Sato I, Shibata T (2001). "Asymmetric autocatalysis and the origin of chiral homogeneity in organic compounds". The Chemical Record. 1 (4): 321–32. doi:10.1002/tcr.1017. PMID11893072.
