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：为了刻画系统中变量间复杂的高阶交互作用，我们提出了一种新的信息熵分解框架，称为系统信息分解（SID）。与部分信息分解（PID）相关方法不同，后者量化单个目标变量与一组源变量之间的交互作用，而SID通过同等审视所有系统变量间的交互作用，扩展了这些方法。具体而言，我们证明了所有信息原子具有对称性，从而确立了SID框架的稳健性，将独特、冗余和协同信息从特定目标变量中剥离出来，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定量方法应遵循的几个性质。进一步地，通过一个示例说明，我们证明了SID能够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，并提供了两种经该案例验证的近似计算方法。高阶度量方面的这一进展使SID能够解释为何整体论认为某些系统在现有度量下无法在不丧失特征的情况下被分解，并为广泛学科中的高阶关系提供了潜在的定量框架。