Information theory is a powerful framework for quantifying complexity, uncertainty, and dynamical structure in time-series data, with widespread applicability across disciplines such as physics, finance, and neuroscience. However, the literature on these measures remains fragmented, with domain-specific terminologies, inconsistent mathematical notation, and disparate visualization conventions that hinder interdisciplinary integration. This work addresses these challenges by unifying key information-theoretic time-series measures through shared semantic definitions, standardized mathematical notation, and cohesive visual representations. We compare these measures in terms of their theoretical foundations, computational formulations, and practical interpretability -- mapping them onto a common conceptual space through an illustrative case study with functional magnetic resonance imaging time series in the brain. This case study exemplifies the complementary insights these measures offer in characterizing the dynamics of complex neural systems, such as signal complexity and information flow. By providing a structured synthesis, our work aims to enhance interdisciplinary dialogue and methodological adoption, which is particularly critical for reproducibility and interoperability in computational neuroscience. More broadly, our framework serves as a resource for researchers seeking to navigate and apply information-theoretic time-series measures to diverse complex systems.

翻译：信息论是一个强大的框架，用于量化时间序列数据中的复杂性、不确定性和动态结构，在物理学、金融学和神经科学等学科中具有广泛适用性。然而，关于这些度量的文献仍然零散，存在领域特定的术语、不一致的数学符号和不同的可视化惯例，阻碍了跨学科整合。本研究通过共享的语义定义、标准化的数学符号和连贯的视觉表示，统一了关键的信息论时间序列度量，以应对这些挑战。我们从理论基础、计算形式和实践可解释性方面比较这些度量——通过一个关于大脑功能磁共振成像时间序列的说明性案例研究，将它们映射到一个共同的概念空间。该案例研究展示了这些度量在表征复杂神经系统的动态特性（如信号复杂性和信息流）时所提供的互补性见解。通过提供一个结构化的综合，我们的工作旨在加强跨学科对话和方法论采用，这对于计算神经科学的可重复性和互操作性尤为关键。更广泛地说，我们的框架为寻求探索和应用信息论时间序列度量于各种复杂系统的研究人员提供了一种资源。