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Since there are no actually infinite systems in the real world, there is no obvious naturally occurring notion of a hard separation between the properties of the constituents of a system and those of the emergent whole. As discussed below, classical mechanics is thought to be emergent from quantum mechanics, though in principle, quantum dynamics fully describes everything happening at a classical level. However, it would take a computer larger than the size of the universe with more computing time than life time of the universe to describe the motion of a falling apple in terms of the locations of its electrons ; thus we can take this to be a "strong" emergent divide.

Since there are no actually infinite systems in the real world, there is no obvious naturally occurring notion of a hard separation between the properties of the constituents of a system and those of the emergent whole. As discussed below, classical mechanics is thought to be emergent from quantum mechanics, though in principle, quantum dynamics fully describes everything happening at a classical level. However, it would take a computer larger than the size of the universe with more computing time than life time of the universe to describe the motion of a falling apple in terms of the locations of its electrons ; thus we can take this to be a "strong" emergent divide.

* [[Classical mechanics]]: The laws of classical mechanics can be said to emerge as a limiting case from the rules of [[quantum mechanics]] applied to large enough masses. This is particularly strange since quantum mechanics is generally thought of as ''more'' complicated than classical mechanics.

* [[Classical mechanics]]: The laws of classical mechanics can be said to emerge as a limiting case from the rules of [[quantum mechanics]] applied to large enough masses. This is particularly strange since quantum mechanics is generally thought of as ''more'' complicated than classical mechanics.

[[经典力学] : 可以说经典力学的法律是从量子力学规则中涌现的，适用于足够大物质的一个极限的例子。这一点特别奇怪，因为人们通常认为量子力学比经典力学更复杂。

* [[经典力学]] : 可以说经典力学的定律是从量子力学定律中涌现的，适用于足够大物质。这一点特别奇怪，因为人们通常认为量子力学比经典力学更复杂。

* [[Friction]]: Forces between elementary particles are conservative. However, friction emerges when considering more complex structures of matter, whose surfaces can convert mechanical energy into heat energy when rubbed against each other. Similar considerations apply to other emergent concepts in [[continuum mechanics]] such as [[viscosity]], [[Elasticity (physics)|elasticity]], [[tensile strength]], etc.

* [[Friction]]: Forces between elementary particles are conservative. However, friction emerges when considering more complex structures of matter, whose surfaces can convert mechanical energy into heat energy when rubbed against each other. Similar considerations apply to other emergent concepts in [[continuum mechanics]] such as [[viscosity]], [[Elasticity (physics)|elasticity]], [[tensile strength]], etc.

Friction: Forces between elementary particles are conservative. However, friction emerges when considering more complex structures of matter, whose surfaces can convert mechanical energy into heat energy when rubbed against each other. Similar considerations apply to other emergent concepts in continuum mechanics such as viscosity, Elasticity (physics)|elasticity, tensile strength, etc.

Friction: Forces between elementary particles are conservative. However, friction emerges when considering more complex structures of matter, whose surfaces can convert mechanical energy into heat energy when rubbed against each other. Similar considerations apply to other emergent concepts in continuum mechanics such as viscosity, Elasticity (physics)|elasticity, tensile strength, etc.

摩擦力: 基本粒子之间的力是''保守的''。然而，当考虑到物质更复杂的结构时，摩擦就涌现了。物质表面相互摩擦时，机械能转化为热能。类似的涌现现象也适用于连续介质力学中的概念，如粘度、弹性、抗拉强度等。

* 摩擦力: 基本粒子之间的力是''[https://baike.baidu.com/item/%E4%BF%9D%E5%AE%88%E5%8A%9B 保守力]''。然而，当考虑到物质更复杂的结构时，摩擦就涌现了。物质表面相互摩擦时，机械能转化为热能。类似的涌现现象也适用于连续介质力学中的概念，如粘度、弹性、抗拉强度等。

* [[Patterned ground]]: the distinct, and often symmetrical geometric shapes formed by ground material in periglacial regions.

* [[Patterned ground]]: the distinct, and often symmetrical geometric shapes formed by ground material in periglacial regions.

Patterned ground: the distinct, and often symmetrical geometric shapes formed by ground material in periglacial regions.

Patterned ground: the distinct, and often symmetrical geometric shapes formed by ground material in periglacial regions.

'''花样表面 Patterned Ground''': 花样表面是在冰缘地区由地面材料形成的明显的，通常是对称的几何图形。

* '''花样表面 Patterned Ground''': 花样表面是在冰缘地区由地面材料形成的明显的，通常是对称的几何图形。

* [[Statistical mechanics]] was initially derived using the concept of a large enough [[statistical ensemble (mathematical physics)|ensemble]] that fluctuations about the most likely distribution can be all but ignored. However, small clusters do not exhibit sharp first order [[phase transition]]s such as melting, and at the boundary it is not possible to completely categorize the cluster as a liquid or solid, since these concepts are (without extra definitions) only applicable to macroscopic systems.  Describing a system using statistical mechanics methods is much simpler than using a low-level atomistic approach.

* [[Statistical mechanics]] was initially derived using the concept of a large enough [[statistical ensemble (mathematical physics)|ensemble]] that fluctuations about the most likely distribution can be all but ignored. However, small clusters do not exhibit sharp first order [[phase transition]]s such as melting, and at the boundary it is not possible to completely categorize the cluster as a liquid or solid, since these concepts are (without extra definitions) only applicable to macroscopic systems.  Describing a system using statistical mechanics methods is much simpler than using a low-level atomistic approach.

Statistical mechanics was initially derived using the concept of a large enough statistical ensemble (mathematical physics)|ensemble that fluctuations about the most likely distribution can be all but ignored. However, small clusters do not exhibit sharp first order phase transitions such as melting, and at the boundary it is not possible to completely categorize the cluster as a liquid or solid, since these concepts are (without extra definitions) only applicable to macroscopic systems.  Describing a system using statistical mechanics methods is much simpler than using a low-level atomistic approach.

Statistical mechanics was initially derived using the concept of a large enough statistical ensemble (mathematical physics)|ensemble that fluctuations about the most likely distribution can be all but ignored. However, small clusters do not exhibit sharp first order phase transitions such as melting, and at the boundary it is not possible to completely categorize the cluster as a liquid or solid, since these concepts are (without extra definitions) only applicable to macroscopic systems.  Describing a system using statistical mechanics methods is much simpler than using a low-level atomistic approach.

统计力学最初是用一个足够大的数学和物理学集合的概念推导出来的，最有可能分布的波动可以是任何事情，但是不可以忽略不计。然而，小的团簇不表现出明显的一级相变，例如熔化，而且在边界上不可能完全将团簇归类为液体或固体，因为这些概念(没有额外的定义)只适用于宏观系统。使用统计力学方法描述一个系统要比使用低层次的原子论方法简单得多。

* 统计力学最初是用一个足够大的统计学集合概念推导出来的，其中概率分布的各种波动可以忽略不计。然而，小的团簇并不会表现出明显的一级相变，例如熔化，而且在边界上不可能完全将团簇归类为液体或固体，因为这些概念(再没有额外的定义的情况下)只适用于宏观系统。使用统计力学方法描述一个系统要比使用低层次的原子论方法简单得多。

* [[Electrical networks]]: The bulk conductive response of binary (RC) electrical networks with random arrangements, known as the [[Universal dielectric response|Universal Dielectric Response (UDR)]], can be seen as emergent properties of such physical systems. Such arrangements can be used as simple physical prototypes for deriving mathematical formulae for the emergent responses of complex systems.<ref>{{cite journal|url = | doi=10.1016/j.physa.2012.10.035 | volume=392 | issue=4 | title=The origin of power-law emergent scaling in large binary networks | year=2013 | journal=Physica A: Statistical Mechanics and Its Applications | pages=1004–1027 | last1 = Almond | first1 = D.P. | last2 = Budd | first2 = C.J. | last3 = Freitag | first3 = M.A. | last4 = Hunt | first4 = G.W. | last5 = McCullen | first5 = N.J. | last6 = Smith | first6 = N.D.| arxiv=1204.5601 | bibcode=2013PhyA..392.1004A }}</ref>

* [[Electrical networks]]: The bulk conductive response of binary (RC) electrical networks with random arrangements, known as the [[Universal dielectric response|Universal Dielectric Response (UDR)]], can be seen as emergent properties of such physical systems. Such arrangements can be used as simple physical prototypes for deriving mathematical formulae for the emergent responses of complex systems.<ref>{{cite journal|url = | doi=10.1016/j.physa.2012.10.035 | volume=392 | issue=4 | title=The origin of power-law emergent scaling in large binary networks | year=2013 | journal=Physica A: Statistical Mechanics and Its Applications | pages=1004–1027 | last1 = Almond | first1 = D.P. | last2 = Budd | first2 = C.J. | last3 = Freitag | first3 = M.A. | last4 = Hunt | first4 = G.W. | last5 = McCullen | first5 = N.J. | last6 = Smith | first6 = N.D.| arxiv=1204.5601 | bibcode=2013PhyA..392.1004A }}</ref>

Electrical networks: The bulk conductive response of binary (RC) electrical networks with random arrangements, known as the Universal Dielectric Response (UDR), can be seen as emergent properties of such physical systems. Such arrangements can be used as simple physical prototypes for deriving mathematical formulae for the emergent responses of complex systems.<ref>

Electrical networks: The bulk conductive response of binary (RC) electrical networks with random arrangements, known as the Universal Dielectric Response (UDR), can be seen as emergent properties of such physical systems. Such arrangements can be used as simple physical prototypes for deriving mathematical formulae for the emergent responses of complex systems.

 

 

 

 

 

Temperature is sometimes used as an example of an emergent macroscopic behaviour. In classical dynamics, a snapshot of the instantaneous momenta of a large number of particles at equilibrium is sufficient to find the average kinetic energy per degree of freedom which is proportional to the temperature. For a small number of particles the instantaneous momenta at a given time are not statistically sufficient to determine the temperature of the system. However, using the ergodic hypothesis, the temperature can still be obtained to arbitrary precision by further averaging the momenta over a long enough time.

Temperature is sometimes used as an example of an emergent macroscopic behaviour. In classical dynamics, a snapshot of the instantaneous momenta of a large number of particles at equilibrium is sufficient to find the average kinetic energy per degree of freedom which is proportional to the temperature. For a small number of particles the instantaneous momenta at a given time are not statistically sufficient to determine the temperature of the system. However, using the ergodic hypothesis, the temperature can still be obtained to arbitrary precision by further averaging the momenta over a long enough time.

温度有时被用来作为一个涌现的宏观行为的例子。在经典动力学中，对处于平衡状态的大量粒子的瞬时动量的捕捉，对于求出每个自由度的平均动能是足够的，而平均动能与温度成正比。对于少数粒子，在给定时间的瞬时动量不足以计算出系统的温度。然而，使用'''遍历假设 Ergodic Hypothesis'''，任意精度的温度仍然可以通过在足够长的时间内进行动量的平均而得到。

* 温度有时被用来作为一个涌现的宏观行为的例子。在经典动力学中，测量到处于平衡状态的大量粒子的瞬时动量就可以求出每个自由度的平均动能，而平均动能与温度成正比。对于少数粒子，在给定时间的瞬时动量不足以计算出系统的温度。然而，使用'''遍历假设 Ergodic Hypothesis'''，任意精度的温度仍然可以通过在足够长的时间内对这少量例子动量的平均而得到。

 

 

Convection in a liquid or gas is another example of emergent macroscopic behaviour that makes sense only when considering differentials of temperature. Convection cells, particularly Bénard cells, are an example of a self-organizing system (more specifically, a dissipative system) whose structure is determined both by the constraints of the system and by random perturbations: the possible realizations of the shape and size of the cells depends on the temperature gradient as well as the nature of the fluid and shape of the container, but which configurations are actually realized is due to random perturbations (thus these systems exhibit a form of symmetry breaking).

Convection in a liquid or gas is another example of emergent macroscopic behaviour that makes sense only when considering differentials of temperature. Convection cells, particularly Bénard cells, are an example of a self-organizing system (more specifically, a dissipative system) whose structure is determined both by the constraints of the system and by random perturbations: the possible realizations of the shape and size of the cells depends on the temperature gradient as well as the nature of the fluid and shape of the container, but which configurations are actually realized is due to random perturbations (thus these systems exhibit a form of symmetry breaking).

液体或气体中的'''对流 Convection'''是另一个涌现宏观行为的例子，只有在考虑温差时才有意义。'''对流细胞 Convection Cells'''，特别是 Bénard 细胞，是一个自组织系统(更具体地说，是一个'''耗散系统 Dissipative System''')的例子，其结构由系统的约束和随机扰动共同决定: 细胞的形状和大小的可能实现取决于温度梯度以及流体的性质和容器的形状，但实际上实现的配置是由于随机扰动(因此这些系统呈现一种'''对称破缺 Symmetry Breaking'''形式)。

* 液体或气体中的'''对流 Convection'''是另一个涌现宏观行为的例子，只有在考虑温差时才有意义。'''对流单体 Convection Cells'''，特别是 Bénard 单体，是一个自组织系统(更具体地说，是一个'''耗散系统 Dissipative System''')的例子，其结构由系统的约束和随机扰动共同决定：细胞的形状和大小可能取决于温度梯度以及流体的性质和容器的形状，但实际上实现的配置是由于随机扰动(因此这些系统呈现一种'''对称破缺 Symmetry Breaking'''形式)。

In some theories of particle physics, even such basic structures as mass, space, and time are viewed as emergent phenomena, arising from more fundamental concepts such as the Higgs boson or strings. In some interpretations of quantum mechanics, the perception of a deterministic reality, in which all objects have a definite position, momentum, and so forth, is actually an emergent phenomenon, with the true state of matter being described instead by a wavefunction which need not have a single position or momentum.

In some theories of particle physics, even such basic structures as mass, space, and time are viewed as emergent phenomena, arising from more fundamental concepts such as the Higgs boson or strings. In some interpretations of quantum mechanics, the perception of a deterministic reality, in which all objects have a definite position, momentum, and so forth, is actually an emergent phenomenon, with the true state of matter being described instead by a wavefunction which need not have a single position or momentum.

在一些粒子物理学理论中，甚至像质量、空间和时间这样的基本结构都被视为来自于更基本的概念（比如'''希格斯玻色子Higgs Boson'''或者'''弦 Strings'''）的涌现现象。在某些量子力学诠释中，对所有物体都具有确定的位置、动量等等的确定性感知，实际上是一种涌现现象，因为物质的真实状态是被不需要单一位置或动量的波函数所描述的。

在一些粒子物理学理论中，甚至是质量、空间和时间这样的基本结构都被视为来自于更基本的概念（比如'''希格斯玻色子 Higgs Boson'''或者'''弦 Strings'''）的涌现现象。在某些量子力学诠释中，对所有物体都具有确定的位置、动量等等的确定性感知，实际上是一种涌现现象，因为物质的真实状态是被波函数所描述的，而这这些波函数不需要单一位置或动量的。

 

Most of the laws of [[physics]] themselves as we experience them today appear to have emerged during the course of time making emergence the most fundamental principle in the universe{{According to whom|date=September 2016}} and raising the question of what might be the most fundamental law of physics from which all others emerged. [[Chemistry]] can in turn be viewed as an emergent property of the laws of physics. [[Biology]] (including biological [[evolution]]) can be viewed as an emergent property of the laws of chemistry. Similarly, [[psychology]] could be understood as an emergent property of neurobiological laws. Finally, free-market theories understand [[economy]] as an emergent feature of psychology.

Most of the laws of [[physics]] themselves as we experience them today appear to have emerged during the course of time making emergence the most fundamental principle in the universe{{According to whom|date=September 2016}} and raising the question of what might be the most fundamental law of physics from which all others emerged. [[Chemistry]] can in turn be viewed as an emergent property of the laws of physics. [[Biology]] (including biological [[evolution]]) can be viewed as an emergent property of the laws of chemistry. Similarly, [[psychology]] could be understood as an emergent property of neurobiological laws. Finally, free-market theories understand [[economy]] as an emergent feature of psychology.

Most of the laws of physics themselves as we experience them today appear to have emerged during the course of time making emergence the most fundamental principle in the universe and raising the question of what might be the most fundamental law of physics from which all others emerged. Chemistry can in turn be viewed as an emergent property of the laws of physics. Biology (including biological evolution) can be viewed as an emergent property of the laws of chemistry. Similarly, psychology could be understood as an emergent property of neurobiological laws. Finally, free-market theories understand economy as an emergent feature of psychology.

Most of the laws of physics themselves as we experience them today appear to have emerged during the course of time making emergence the most fundamental principle in the universe and raising the question of what might be the most fundamental law of physics from which all others emerged. Chemistry can in turn be viewed as an emergent property of the laws of physics. Biology (including biological evolution) can be viewed as an emergent property of the laws of chemistry. Similarly, psychology could be understood as an emergent property of neurobiological laws. Finally, free-market theories understand economy as an emergent feature of psychology.

我们今天所经历的大多数物理定律，似乎都是在时间的推移中出现的，这使得涌现成为宇宙中最基本的定律，同时出现了一个问题: 什么可能是物理学中最基本的定律，而其他所有定律都是从这个定律中涌现而来的。化学可以被看作是物理定律的一种涌现。生物学(包括生物进化)可以看作是化学定律的涌现。同样，心理学也可以被理解为神经生物学定律的一种涌现。最后，经济学中的自由市场理论是心理学的一个涌现。

我们今天所经历的大多数物理定律，似乎都是在时间的推移中出现的，这使得涌现成为宇宙中最基本的定律，同时出现了一个问题：什么可能是物理学中最基本的定律，而其他所有定律都是从这个定律中涌现而来的？化学可以被看作是物理定律的一种涌现。生物学(包括生物进化)可以看作是化学定律的涌现。同样，心理学也可以被理解为神经生物学定律的一种涌现。最后，经济学中的自由市场理论是心理学的一个涌现。

 

 

According to Laughlin (2005), for many particle systems, nothing can be calculated exactly from the microscopic equations, and macroscopic systems are characterised by broken symmetry: the symmetry present in the microscopic equations is not present in the macroscopic system, due to phase transitions. As a result, these macroscopic systems are described in their own terminology, and have properties that do not depend on many microscopic details. This does not mean that the microscopic interactions are irrelevant, but simply that you do not see them anymore&nbsp;— you only see a renormalized effect of them. Laughlin is a pragmatic theoretical physicist: if you cannot, possibly ever, calculate the broken symmetry macroscopic properties from the microscopic equations, then what is the point of talking about reducibility?

According to Laughlin (2005), for many particle systems, nothing can be calculated exactly from the microscopic equations, and macroscopic systems are characterised by broken symmetry: the symmetry present in the microscopic equations is not present in the macroscopic system, due to phase transitions. As a result, these macroscopic systems are described in their own terminology, and have properties that do not depend on many microscopic details. This does not mean that the microscopic interactions are irrelevant, but simply that you do not see them anymore&nbsp;— you only see a renormalized effect of them. Laughlin is a pragmatic theoretical physicist: if you cannot, possibly ever, calculate the broken symmetry macroscopic properties from the microscopic equations, then what is the point of talking about reducibility?

Laughlin(2005)认为，对于许多粒子系统来说，从微观方程中无法精确地计算出任何东西，宏观系统是通过破缺的对称性来刻画: 由于相变的存在，微观方程中存在的对称性无法在宏观系统中存在。因此，这些宏观系统需要用它们自己的术语来描述，并且具有许多不依赖微观细节的性质。这并不意味着宏观性质和微观的相互作用无关，只是你不再看到它们了，你只看到它们的'''重整化效应 Renormalized Effect'''。Laughlin是一个务实的理论物理学家: 如果你不能从微观尺度的方程中计算出对称性破缺的宏观性质，那么谈论'''还原性 Reducibility'''还有什么意义？

Laughlin(2005)认为，对于许多粒子系统来说，从微观方程中无法精确地计算出任何东西，宏观系统是通过破缺的对称性来刻画: 由于相变的存在，微观方程中存在的对称性无法在宏观系统中存在。因此，这些宏观系统需要用它们自己的术语来描述，并且具有许多不依赖微观细节的性质。这并不意味着宏观性质和微观的相互作用无关，只是你不再看到它们了，你只看到它们的'''重整化效应 Renormalized Effect'''。Laughlin是一个务实的理论物理学家：如果你不能从微观尺度的方程中计算出对称性破缺的宏观性质，那么谈论'''还原性 Reducibility'''还有什么意义？

===生命，生物系统===

===生命，生物系统===