标题： 通过有效信息分解量化系统-环境协同信息 显示英文标题

标题： Quantifying system-environment synergistic information by effective information decomposition

摘要： 生命系统最重要的特征是什么？ 目前，许多理论试图解释生命系统与一般系统之间的本质区别，例如自组织理论和自由能原理，但缺乏一个合理的指标来衡量一个系统在多大程度上可以被视为具有生命特征的系统，尤其是对生命系统的动态特征关注不足。 在本文中，我们提出了一种在动态机制层面的新指标，用于衡量系统对环境灵活响应的能力。 我们证明了该指标满足部分信息分解（PID）框架中的多元信息分解公理体系。 通过对该指标的进一步分解和分析，我们发现它取决于系统与环境变量在动态中的纠缠程度以及噪声的大小。 我们对细胞自动机（CA）、随机布尔网络和真实的基因调控网络（GRN）进行了测量，验证了其与CA类型和兰顿参数的关系，并确定在GRN中反馈环具有灵活响应环境的高能力。 我们还结合了机器学习技术，证明该框架可以应用于未知动力学的情况。 显示英文摘要

摘要： What is the most crucial characteristic of a system with life activity? Currently, many theories have attempted to explain the most essential difference between living systems and general systems, such as the self-organization theory and the free energy principle, but there is a lack of a reasonable indicator that can measure to what extent a system can be regarded as a system with life characteristics, especially the lack of attention to the dynamic characteristics of life systems. In this article, we propose a new indicator at the level of dynamic mechanisms to measure the ability of a system to flexibly respond to the environment. We proved that this indicator satisfies the axiom system of multivariate information decomposition in the partial information decomposition (PID) framework. Through further disassembly and analysis of this indicator, we found that it is determined by the degree of entanglement between system and environmental variables in the dynamics and the magnitude of noise. We conducted measurements on cellular automata (CA), random Boolean networks, and real gene regulatory networks (GRN), verified its relationship with the type of CA and the Langton parameter, and identified that the feedback loops have high abilities to flexibly respond to the environment on the GRN. We also combined machine learning technology to prove that this framework can be applied in the case of unknown dynamics.