In the 21st century, many of the crucial scientific and technical issues facing humanity can be understood as problems associated with understanding, modelling, and ultimately controlling complex systems: systems comprised of a large number of non-trivially interacting components whose collective behaviour can be difficult to predict. Information theory, a branch of mathematics historically associated with questions about encoding and decoding messages, has emerged as something of a lingua franca for those studying complex systems, far exceeding its original narrow domain of communication systems engineering. In the context of complexity science, information theory provides a set of tools which allow researchers to uncover the statistical and effective dependencies between interacting components; relationships between systems and their environment; mereological whole-part relationships; and is sensitive to non-linearities missed by commonly parametric statistical models. In this review, we aim to provide an accessible introduction to the core of modern information theory, aimed specifically at aspiring (and established) complex systems scientists. This includes standard measures, such as Shannon entropy, relative entropy, and mutual information, before building to more advanced topics, including: information dynamics, measures of statistical complexity, information decomposition, and effective network inference. In addition to detailing the formal definitions, in this review we make an effort to discuss how information theory can be interpreted and develop the intuition behind abstract concepts like "entropy," in the hope that this will enable interested readers to understand what information is, and how it is used, at a more fundamental level.

翻译：在21世纪，人类面临的许多关键科学和技术问题可被理解为理解、建模并最终控制复杂系统所关联的难题：这类系统由大量具有非平凡交互作用的组件构成，其集体行为往往难以预测。信息论——一门历史上与消息编解码问题相关的数学分支——已超越其最初狭隘的通信系统工程领域，成为复杂系统研究者的事实通用语言。在复杂性科学语境中，信息论提供了一套工具，使研究者能够揭示交互组件间的统计与有效依赖关系、系统与其环境之间的关联、部分-整体层级关系，并对常见参数化统计模型难以捕捉的非线性特征具有敏感性。本综述旨在面向有志于（及已有建树的）复杂系统科学家，提供现代信息论核心的可读性导引。内容涵盖标准度量（如香农熵、相对熵和互信息），进而延伸至更高级主题：信息动力学、统计复杂度度量、信息分解及有效网络推断。除详述形式化定义外，我们亦致力于探讨信息论的解释方式，并培养对"熵"等抽象概念的直觉理解，以期帮助感兴趣的读者在更深层次上理解信息是什么以及如何被运用。