To characterize the complex higher-order interactions among variables within a system, this study introduces a novel framework, termed System Information Decomposition (SID), aimed at decomposing the information entropy of variables into information atoms based on their interrelations. Diverging from the established Partial Information Decomposition (PID) framework, which predominantly concentrates on the directional interactions stemming from an array of source variables to a single target variable, SID adopts a holistic approach, scrutinizing the interactions across all variables within the system. Specifically, we proved all the information atoms are symmetric, which means the disentanglement of unique, redundant, and synergistic information from any specific target variable. Hence, our proposed SID framework can capture the symmetric pairwise and higher-order relationships among variables. This advance positions SID as a promising framework with the potential to foster a deeper understanding of higher-order relationships within complex systems across disciplines.

翻译：为描述系统内变量间复杂的高阶交互作用，本研究提出了一种名为"系统信息分解"(SID)的新框架，旨在基于变量间的相互关系将其信息熵分解为信息原子。与主要关注源变量集合对单个目标变量方向性交互的已确立的偏信息分解(PID)框架不同，SID采用整体视角，审视系统内所有变量间的交互作用。具体而言，我们证明了所有信息原子均具有对称性，这意味着可从任意特定目标变量中解耦出独特信息、冗余信息和协同信息。因此，所提出的SID框架能够捕捉变量间的对称性成对及高阶关系。这一进展使SID成为一个具有潜力的框架，有望促进跨学科领域对复杂系统中高阶关系的深入理解。