自组织到相变边缘的反馈机制
Feedback mechanisms for self-organization to the edge of a phase transition
摘要：
在物理、地质和生物系统中经常观察到无尺度的活动爆发。自组织临界性（SOC）的概念，早在1987年由Bak，Tang和Wiesenfeld提出，表明在某些情况下，自然系统似乎可以自我调节到临界状态，伴随着幂律和缩放。理论上的进步使SOC的工作原理合理化，它将SOC的临界特性与标准的非平衡二阶相变的临界特性联系起来，这种相变将动态活动无限期地回荡的活动状态与活动最终停止的吸收或静止状态分开。在这里，我们简要地回顾这些想法以及最近密切相关的概念：自组织双稳态（自组织双稳态）。在双稳态中，非常相同类型的反馈在以不连续的相变为特征的系统中操作，其没有临界点，而是呈现活动状态和静止状态之间的双稳态。大爆发也会导致活动的尺度不变的雪崩，但在这种情况下，它具有不同类型的尺度，并与巨大的爆发共存。此外，STEM解释实验与真正的沙堆比SOC更密切。我们回顾SOC和STEM之间的异同，提出和分析它们在一个共同的理论框架下，包括最近的结果，以及可能的未来发展。我们还讨论了其他相关的概念“不完美”的自组织，如“自组织准临界性”和“自组织集体振荡”，在例如神经科学的相关性，提供一个概述的反馈机制的自组织的边缘的相变的目的。
英文摘要：
Scale-free outbursts of activity are commonly observed in physical, geological, and biological systems. The idea of self-organized criticality (SOC), introduced back in 1987 by Bak, Tang and Wiesenfeld suggests that, under certain circumstances, natural systems can seemingly self-tune to a critical state with its concomitant power-laws and scaling. Theoretical progress allowed for a rationalization of how SOC works by relating its critical properties to those of a standard non-equilibrium second-order phase transition that separates an active state in which dynamical activity reverberates indefinitely, from an absorbing or quiescent state where activity eventually ceases. Here, we briefly review these ideas as well as a recent closely-related concept: self-organized bistability (SOB). In SOB, the very same type of feedback operates in a system characterized by a discontinuos phase transition, which has no critical point but instead presents bistability between active and quiescent states. SOB also leads to scale-invariant avalanches of activity but, in this case, with a different type of scaling and coexisting with anomalously large outbursts. Moreover, SOB explains experiments with real sandpiles more closely than SOC. We review similarities and differences between SOC and SOB by presenting and analyzing them under a common theoretical framework, covering recent results as well as possible future developments. We also discuss other related concepts for "imperfect" self-organization such as "self-organized quasi-criticality" and "self-organized collective oscillations", of relevance in e.g. neuroscience, with the aim of providing an overview of feedback mechanisms for self-organization to the edge of a phase transition.
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