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. The basic mechanism underlying SOC is the alternation of a slow driving process and fast dynamics with dissipation, which generates a feedback loop that tunes the system to the critical point of an absorbing-active continuous phase transition. 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 discontinuous 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.

通常在物理，地质和生物系统中观察到无鳞的活动爆发。Bak，Tang和Wiesenfeld于1987年提出的自组织临界度（SOC）概念表明，在某些情况下，自然系统似乎可以通过其伴随的幂律和定标自调整为临界状态。理论上的进步通过将SOC的临界特性与标准非平衡二阶相变的临界特性相关联，从而合理化了SOC的工作原理，该标准非平衡二阶相变将活跃状态（其中动态活动无限期回荡）与吸收或静止状态（最终活动停止）分开。SOC的基本机制是慢速驱动过程和带耗散的快速动态的交替，它会产生一个反馈环路，该环路将系统调整到吸收活性连续相变的临界点。在这里，我们简要回顾这些想法以及最近紧密相关的概念：自组织双稳态（SOB）。在SOB中，相同类型的反馈在以不连续相变为特征的系统中运行，该相变没有临界点，而是呈现出活动状态和静止状态之间的双稳态。SOB还导致活动的规模不变雪崩，但在这种情况下，具有不同类型的规模，并与异常大爆发共存。此外，SOB比SOC更能说明真实沙堆的实验。我们通过在共同的理论框架下介绍和分析SOC和SOB之间的异同来回顾它们，涵盖最近的结果以及未来可能的发展。我们还将讨论其他与“不完美”自组织有关的概念，例如“自组织准临界性”和“自组织集体振荡”，例如在神经科学领域的相关性，目的是概述针对自组织到相变边缘。