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此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。In [[physics]], '''self-organized criticality''' ('''SOC''') is a property of [[dynamical system]]s that have a [[critical phenomena|critical point]] as an [[attractor]].  Their macroscopic behavior thus displays the spatial or temporal [[scale invariance|scale-invariance]] characteristic of the [[critical point (physics)|critical point]] of a [[phase transition]], but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves towards criticality.

In [[physics]], '''self-organized criticality''' ('''SOC''') is a property of [[dynamical system]]s that have a [[critical phenomena|critical point]] as an [[attractor]].  Their macroscopic behavior thus displays the spatial or temporal [[scale invariance|scale-invariance]] characteristic of the [[critical point (physics)|critical point]] of a [[phase transition]], but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves towards criticality.

In physics, self-organized criticality (SOC) is a property of dynamical systems that have a critical point as an attractor.  Their macroscopic behavior thus displays the spatial or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves towards criticality.

In physics, self-organized criticality (SOC) is a property of dynamical systems that have a critical point as an attractor.  Their macroscopic behavior thus displays the spatial or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves towards criticality.

== Overview ==

== Overview 概览==

Self-organized criticality is one of a number of important discoveries made in statistical physics and related fields over the latter half of the 20th century, discoveries which relate particularly to the study of complexity in nature.  For example, the study of cellular automata, from the early discoveries of Stanislaw Ulam and John von Neumann through to John Conway's Game of Life and the extensive work of Stephen Wolfram, made it clear that complexity could be generated as an emergent feature of extended systems with simple local interactions.  Over a similar period of time, Benoît Mandelbrot's large body of work on fractals showed that much complexity in nature could be described by certain ubiquitous mathematical laws, while the extensive study of phase transitions carried out in the 1960s and 1970s showed how scale invariant phenomena such as fractals and power laws emerged at the critical point between phases.

Self-organized criticality is one of a number of important discoveries made in statistical physics and related fields over the latter half of the 20th century, discoveries which relate particularly to the study of complexity in nature.  For example, the study of cellular automata, from the early discoveries of Stanislaw Ulam and John von Neumann through to John Conway's Game of Life and the extensive work of Stephen Wolfram, made it clear that complexity could be generated as an emergent feature of extended systems with simple local interactions.  Over a similar period of time, Benoît Mandelbrot's large body of work on fractals showed that much complexity in nature could be described by certain ubiquitous mathematical laws, while the extensive study of phase transitions carried out in the 1960s and 1970s showed how scale invariant phenomena such as fractals and power laws emerged at the critical point between phases.

自组织临界性是20世纪下半叶统计物理学及相关领域的众多重要发现之一，这些发现尤其与研究自然界的复杂性有关。例如，细胞自动机的研究---- 从 Stanislaw Ulam 和约翰·冯·诺伊曼的早期发现到 John Conway 的《生命的游戏》和 Stephen Wolfram 的大量工作---- 清楚地表明，复杂性可以作为具有简单局部相互作用的扩展系统的一个涌现特征而产生。在相似的时间段内，beno t Mandelbrot 关于分形的大量工作表明，自然界的许多复杂性可以用某些无处不在的数学定律来描述，而在20世纪60年代和70年代对相变的广泛研究表明，诸如分形和幂定律等尺度不变现象是如何出现在相变的临界点上的。

'''<font color="#ff8000"> 自组织临界性Self-organized criticality（SOC)</font>'''是20世纪下半叶统计物理学及相关领域的众多重要发现之一，这些发现尤其与研究自然界的复杂性有关。例如，细胞自动机的研究---- 从 Stanislaw Ulam 和约翰·冯·诺伊曼的早期发现到 John Conway 的《生命的游戏》和 Stephen Wolfram 的大量工作---- 清楚地表明，复杂性可以作为具有简单局部相互作用的扩展系统的一个涌现特征而产生。在相似的时间段内，beno t Mandelbrot 关于分形的大量工作表明，自然界的许多复杂性可以用某些无处不在的数学定律来描述，而在20世纪60年代和70年代对相变的广泛研究表明，诸如分形和幂定律等尺度不变现象是如何出现在相变的临界点上的。

The term self-organized criticality was firstly introduced by Bak, Tang and Wiesenfeld's 1987 paper, which clearly linked together those factors: a simple cellular automaton was shown to produce several characteristic features observed in natural complexity (fractal geometry, pink (1/f) noise and power laws) in a way that could be linked to critical-point phenomena. Crucially, however, the paper emphasized that the complexity observed emerged in a robust manner that did not depend on finely tuned details of the system: variable parameters in the model could be changed widely without affecting the emergence of critical behavior: hence, self-organized criticality. Thus, the key result of BTW's paper was its discovery of a mechanism by which the emergence of complexity from simple local interactions could be spontaneous&mdash;and therefore plausible as a source of natural complexity&mdash;rather than something that was only possible in artificial situations in which control parameters are tuned to precise critical values. The publication of this research sparked considerable interest from both theoreticians and experimentalists, producing some of the most cited papers in the scientific literature.

The term self-organized criticality was firstly introduced by Bak, Tang and Wiesenfeld's 1987 paper, which clearly linked together those factors: a simple cellular automaton was shown to produce several characteristic features observed in natural complexity (fractal geometry, pink (1/f) noise and power laws) in a way that could be linked to critical-point phenomena. Crucially, however, the paper emphasized that the complexity observed emerged in a robust manner that did not depend on finely tuned details of the system: variable parameters in the model could be changed widely without affecting the emergence of critical behavior: hence, self-organized criticality. Thus, the key result of BTW's paper was its discovery of a mechanism by which the emergence of complexity from simple local interactions could be spontaneous&mdash;and therefore plausible as a source of natural complexity&mdash;rather than something that was only possible in artificial situations in which control parameters are tuned to precise critical values. The publication of this research sparked considerable interest from both theoreticians and experimentalists, producing some of the most cited papers in the scientific literature.

自组织临界性这个术语最早由 Bak，Tang 和 Wiesenfeld 在1987年的论文中提出，这篇论文将这些因素清楚地联系在一起: 一个简单的细胞自动机被证明可以产生在自然复杂性中观察到的几个特征(分形几何、粉红噪声和幂定律) ，这种方式可以与临界点现象联系起来。然而，关键的是，这篇论文强调，观察到的复杂性是以一种强有力的方式出现的，并不依赖于系统精细调整的细节: 模型中的可变参数可以被广泛改变，而不会影响关键行为的出现: 因此，自组织临界性。因此，BTW 论文的关键结果是发现了一种机制，通过这种机制，从简单的局部相互作用中产生的复杂性可能是自发的---- 因此是合理的自然复杂性的来源---- 而不是只有在控制参数调整到精确的临界值的人工情况下才可能出现的东西。这项研究的发表引起了理论家和实验家的极大兴趣，产生了一些在科学文献中被引用最多的论文。

'''<font color="#ff8000"> 自组织临界性Self-organized criticality（SOC)</font>'''这个术语最早由 Bak，Tang 和 Wiesenfeld 在1987年的论文中提出，这篇论文将这些因素清楚地联系在一起: 一个简单的细胞自动机被证明可以产生在自然复杂性中观察到的几个特征(分形几何、粉红噪声和幂定律) ，这种方式可以与临界点现象联系起来。然而，关键的是，这篇论文强调，观察到的复杂性是以一种强有力的方式出现的，并不依赖于系统精细调整的细节: 模型中的可变参数可以被广泛改变，而不会影响关键行为的出现: 因此，自组织临界性。因此，BTW 论文的关键结果是发现了一种机制，通过这种机制，从简单的局部相互作用中产生的复杂性可能是自发的---- 因此是合理的自然复杂性的来源---- 而不是只有在控制参数调整到精确的临界值的人工情况下才可能出现的东西。这项研究的发表引起了理论家和实验家的极大兴趣，产生了一些在科学文献中被引用最多的论文。

</ref>), and examination of the conditions necessary for SOC to emerge. One of the important issues for the latter investigation was whether conservation of energy was required in the local dynamical exchanges of models: the answer in general is no, but with (minor) reservations, as some exchange dynamics (such as those of BTW) do require local conservation at least on average.  In the long term, key theoretical issues yet to be resolved include the calculation of the possible universality classes of SOC behavior and the question of whether it is possible to derive a general rule for determining if an arbitrary algorithm displays SOC.

</ref>), and examination of the conditions necessary for SOC to emerge. One of the important issues for the latter investigation was whether conservation of energy was required in the local dynamical exchanges of models: the answer in general is no, but with (minor) reservations, as some exchange dynamics (such as those of BTW) do require local conservation at least on average.  In the long term, key theoretical issues yet to be resolved include the calculation of the possible universality classes of SOC behavior and the question of whether it is possible to derive a general rule for determining if an arbitrary algorithm displays SOC.

/ ref) ，以及研究出现 SOC 的必要条件。后一项研究的一个重要问题是，在局部动态交换模型时是否需要能量守恒: 一般的答案是否定的，但有一些保留意见，因为一些交换动态(如 BTW 的动态)确实需要局部至少平均的能量守恒。从长远来看，有待解决的关键理论问题包括 SOC 行为可能的普适性类的计算，以及是否有可能推导出一个确定任意算法是否显示 SOC 的一般规则的问题。

/ ref) ，以及研究出现 '''<font color="#ff8000"> SOC</font>'''的必要条件。后一项研究的一个重要问题是，在局部动态交换模型时是否需要能量守恒: 一般的答案是否定的，但有一些保留意见，因为一些交换动态(如 BTW 的动态)确实需要局部至少平均的能量守恒。从长远来看，有待解决的关键理论问题包括 '''<font color="#ff8000"> SOC</font>''' 行为可能的普适性类的计算，以及是否有可能推导出一个确定任意算法是否显示 '''<font color="#ff8000"> SOC</font>''' 的一般规则的问题。

Alongside these largely lab-based approaches, many other investigations have centered around large-scale natural or social systems that are known (or suspected) to display scale-invariant behavior.  Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: earthquakes (which, long before SOC was discovered, were known as a source of scale-invariant behavior such as the Gutenberg–Richter law describing the statistical distribution of earthquake size, and the Omori law describing the frequency of aftershocks<ref name=TurcotteSmalleySolla85>

Alongside these largely lab-based approaches, many other investigations have centered around large-scale natural or social systems that are known (or suspected) to display scale-invariant behavior.  Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: earthquakes (which, long before SOC was discovered, were known as a source of scale-invariant behavior such as the Gutenberg–Richter law describing the statistical distribution of earthquake size, and the Omori law describing the frequency of aftershocks<ref name=TurcotteSmalleySolla85>

除了这些大部分基于实验室的方法，许多其他的研究都集中在大规模的自然或社会系统上，这些系统已经知道(或怀疑)表现出尺度不变的行为。虽然这些方法并不总是受到研究对象专家的欢迎(至少最初是这样) ，但 SOC 已经成为解释一些自然现象的强有力的候选者，包括: 地震(早在 SOC 被发现之前，地震就被认为是尺度不变行为的来源，例如描述地震大小统计分布的古腾堡-里克特定律，以及描述余震频率的描述余震的 Omori 定律，命名为 turcottesmalleysolla85

除了这些大部分基于实验室的方法，许多其他的研究都集中在大规模的自然或社会系统上，这些系统已经知道(或怀疑)表现出尺度不变的行为。虽然这些方法并不总是受到研究对象专家的欢迎(至少最初是这样) ，但 '''<font color="#ff8000"> SOC</font>''' 已经成为解释一些自然现象的强有力的候选者，包括: 地震(早在 '''<font color="#ff8000"> SOC</font>''' 被发现之前，地震就被认为是尺度不变行为的来源，例如描述地震大小统计分布的古腾堡-里克特定律，以及描述余震频率的描述余震的 Omori 定律，命名为 turcottesmalleysolla85

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An example of such an optimization problem is graph coloring. The SOC process apparently helps the optimization from getting stuck in a local optimum without the use of any annealing scheme, as suggested by previous work on extremal optimization.

An example of such an optimization problem is graph coloring. The SOC process apparently helps the optimization from getting stuck in a local optimum without the use of any annealing scheme, as suggested by previous work on extremal optimization.

图着色就是这种最佳化问题的一个例子。Soc 过程显然有助于优化陷入局部最优，而无需使用任何退火方案，正如以前的极值优化工作所建议的。

图着色就是这种最佳化问题的一个例子。'''<font color="#ff8000"> SOC</font>''' 过程显然有助于优化陷入局部最优，而无需使用任何退火方案，正如以前的极值优化工作所建议的。

The recent excitement generated by scale-free networks has raised some interesting new questions for SOC-related research: a number of different SOC models have been shown to generate such networks as an emergent phenomenon, as opposed to the simpler models proposed by network researchers where the network tends to be assumed to exist independently of any physical space or dynamics. While many single phenomena have been shown to exhibit scale-free properties over narrow ranges, a phenomenon offering by far a larger amount of data is solvent-accessible surface areas in globular proteins.<ref name=Moret2007>

The recent excitement generated by scale-free networks has raised some interesting new questions for SOC-related research: a number of different SOC models have been shown to generate such networks as an emergent phenomenon, as opposed to the simpler models proposed by network researchers where the network tends to be assumed to exist independently of any physical space or dynamics. While many single phenomena have been shown to exhibit scale-free properties over narrow ranges, a phenomenon offering by far a larger amount of data is solvent-accessible surface areas in globular proteins.<ref name=Moret2007>

无标度网络最近引起的兴奋为 SOC 相关研究提出了一些有趣的新问题: 许多不同的 SOC 模型已经被证明是作为一种涌现现象产生这样的网络，而不是网络研究人员提出的更简单的模型，其中网络往往被假定独立于任何物理空间或动力学存在。虽然许多单一现象已被证明在狭窄的范围内表现出无标度特性，但是到目前为止提供了大量数据的现象是球状蛋白质中溶剂可及的表面区域。 参考名称 moret2007

'''<font color="#ff8000"> 无标度网络Scale-free networks</font>'''最近引起的兴奋为 '''<font color="#ff8000"> SOC</font>'''相关研究提出了一些有趣的新问题: 许多不同的 '''<font color="#ff8000"> SOC</font>'''模型已经被证明是作为一种涌现现象产生这样的网络，而不是网络研究人员提出的更简单的模型，其中网络往往被假定独立于任何物理空间或动力学存在。虽然许多单一现象已被证明在狭窄的范围内表现出无标度特性，但是到目前为止提供了大量数据的现象是球状蛋白质中溶剂可及的表面区域。 参考名称 moret2007

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  }}</ref> A continuous model of self-organised criticality is proposed by using tropical geometry.

  }}</ref> A continuous model of self-organised criticality is proposed by using tropical geometry.

{} / ref 一个自组织临界的连续模型是通过使用热带几何来提出的。

{} / ref 一个'''<font color="#ff8000"> 自组织临界Self-organised criticality</font>'''的连续模型是通过使用热带几何来提出的。

== Examples of self-organized critical dynamics ==

== Examples of self-organized critical dynamics自组织临界动力学的例子 ==

== See also ==

== See also 参见==

==References==

==References参考资料==

== Further reading ==

== Further reading延伸阅读 ==

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