In order to characterize complex higher-order interactions among variables in a system, we introduce a new framework for decomposing the information entropy of variables in a system, termed System Information Decomposition (SID). Diverging from Partial Information Decomposition (PID) correlation methods, which quantify the interaction between a single target variable and a collection of source variables, SID extends those approaches by equally examining the interactions among all system variables. Specifically, we establish the robustness of the SID framework by proving all the information atoms are symmetric, which detaches the unique, redundant, and synergistic information from the specific target variable, empowering them to describe the relationship among variables. Additionally, we analyze the relationship between SID and existing information measures and propose several properties that SID quantitative methods should follow. Furthermore, by employing an illustrative example, we demonstrate that SID uncovers a higher-order interaction relationships among variables that cannot be captured by current measures of probability and information and provide two approximate calculation methods verified by this case. This advance in higher-order measures enables SID to explain why Holism posits that some systems cannot be decomposed without loss of characteristics under existing measures, and offers a potential quantitative framework for higher-order relationships across a broad spectrum of disciplines.

翻译：为刻画系统中变量间复杂的高阶交互关系，我们提出了一种对系统变量信息熵进行分解的新框架，称为系统信息分解（System Information Decomposition, SID）。与通过量化单一目标变量与源变量集合间交互的局部信息分解（Partial Information Decomposition, PID）相关方法不同，SID 通过同等考察所有系统变量间的交互来扩展这些方法。具体地，我们通过证明所有信息原子均具有对称性来确立 SID 框架的稳健性，从而将独特信息、冗余信息和协同信息从特定目标变量中剥离，使其能够描述变量间的关系。此外，我们分析了 SID 与现有信息度量之间的关系，并提出了 SID 定量方法应遵循的若干性质。进一步地，通过一个示例，我们证明 SID 能揭示当前概率与信息度量无法捕捉的变量间高阶交互关系，并据此案例提供了两种近似计算方法。这一高阶度量方面的进展使 SID 能够阐释整体论（Holism）所提出的"某些系统在现有度量下无法在不丢失特征的情况下被分解"的观点，并为跨学科领域中高阶关系的研究提供了潜在的定量框架。