Criticality is thought to be crucial for complex systems to adapt at the boundary between regimes with different dynamics, where the system may transition from one phase to another. Numerous systems, from sandpiles to gene regulatory networks to swarms to human brains, seem to work towards preserving a precarious balance right at their critical point. Understanding criticality therefore seems strongly related to a broad, fundamental theory for the physics of life as it could be, which still lacks a clear description of how life can arise and maintain itself in complex systems. In order to investigate this crucial question, we model populations of Ising agents competing for resources in a simple 2D environment subject to an evolutionary algorithm. We then compare its evolutionary dynamics under different experimental conditions. We demonstrate the utility that arises at a critical state and contrast it with the behaviors and dynamics that arise far from criticality. The results show compelling evidence that not only is a critical state remarkable in its ability to adapt and find solutions to the environment, but the evolving parameters in the agents tend to flow towards criticality if starting from a supercritical regime. We present simulations showing that a system in a supercritical state will tend to self-organize towards criticality, in contrast to a subcritical state, which remains subcritical though it is still capable of adapting and increasing its fitness.

中文翻译：

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进化到 Ising 神经代理的关键性

临界性被认为对于复杂系统适应具有不同动态的制度之间的边界至关重要，系统可能会从一个阶段过渡到另一个阶段。许多系统，从沙堆到基因调控网络，再到蜂群到人脑，似乎都在努力在关键点保持不稳定的平衡。因此，理解临界性似乎与生命物理学​​的广泛、基本理论密切相关，它仍然缺乏对生命如何在复杂系统中产生和维持自身的清晰描述。为了研究这个关键问题，我们在一个简单的 2D 环境中根据进化算法对竞争资源的 Ising 代理群体进行建模。然后我们比较了它在不同实验条件下的进化动力学。我们展示了在临界状态下出现的效用，并将其与远离临界状态的行为和动态进行对比。结果显示令人信服的证据表明，临界状态不仅在适应环境和寻找环境解决方案的能力方面表现出色，而且如果从超临界状态开始，代理中不断变化的参数往往会趋向临界状态。我们提供的模拟表明，处于超临界状态的系统将倾向于自组织朝向临界状态，这与亚临界状态相反，亚临界状态仍然是亚临界状态，尽管它仍然能够适应和增加其适应度。结果显示令人信服的证据表明，临界状态不仅在适应环境和寻找环境解决方案的能力方面表现出色，而且如果从超临界状态开始，代理中不断变化的参数往往会趋向临界状态。我们提供的模拟表明，处于超临界状态的系统将倾向于自组织朝向临界状态，这与亚临界状态相反，亚临界状态仍然是亚临界状态，尽管它仍然能够适应和增加其适应度。结果显示令人信服的证据表明，临界状态不仅在适应环境和寻找环境解决方案的能力方面表现出色，而且如果从超临界状态开始，代理中不断变化的参数往往会趋向临界状态。我们提供的模拟表明，处于超临界状态的系统将倾向于自组织朝向临界状态，这与亚临界状态相反，亚临界状态仍然是亚临界状态，尽管它仍然能够适应和增加其适应度。