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：为刻画系统内变量间复杂的高阶交互作用，本研究提出了一种称为系统信息分解（SID）的新框架，旨在将变量的信息熵依据其相互关系分解为信息原子。与主要关注从一系列源变量到单个目标变量定向交互作用的现有偏信息分解（PID）框架不同，SID采用整体性方法，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，这意味着可从任何特定目标变量中解耦出独特、冗余与协同信息。因此，我们所提出的SID框架能够捕捉变量间对称的成对及高阶关系。这一进展使SID成为一个有前景的框架，有望促进跨学科领域对复杂系统内高阶关系的更深入理解。