更改

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

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

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。

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.

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/>

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。

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。

===背景===

===背景===

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.

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。

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。

 

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。  

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。  

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.

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  

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>.

.

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]].

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]].

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>

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。

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。

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

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

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

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

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

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

:<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>

:<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>.

布鲁塞尔振子有一个固定点

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 ====

 

 

 

 

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

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示例是Brusselator(参见Prigogine参考)。它的特征是反应

另一个演示时间顺序的系统示例是Brusselator(参见Prigogine参考)。它的特征是反应.

 

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

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

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

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

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

 

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

 

 

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

 

 

 

 

:<math>  X \rightarrow E</math>

:<math>  X \rightarrow E</math>

with the rate equations

with the rate equations