关键词：信息论、熵、互信息、传递熵、整合信息（Φ）、部分信息分解（PID / PED）、O-信息 / Φᵣ、多尺度动力学 无论是气候变化、流行病传播、金融市场波动，还是大脑的认知功能，这些系统都由大量组件构成，组件间存在多样且动态的互动，因为这些 非平凡的互动具有如非线性、涌现、自适应和路径依赖等特征，导致其集体行为往往难以通过还原论预测。面对这些错综复杂的涌现现象，科 学家们迫切需要一套强大而普适的数学语言来对其进行描述、量化和理解。 起源于通信的信息论，因其能跨领域量化组件之间，系统与环境，整体与部分的互动，正逐渐成为复杂系统研究领域工具箱中不可或缺的一 环。本文旨在对Thomas F. Varley于2025年12月8日发表在《Physics Reports》上的这篇重要综述进行深入解读，系统阐述信息理论为何以及如何 成为复杂系统科学的基石，并详解其核心概念、进阶工具与实际应用。 想象一个天气预报。如果某地一年365天都是晴天，那么你对"明天天气"的不确定性为零，熵也为零。如果天气晴雨各半，你的不确定性最大，熵也最 高。因此，熵衡量的是在得知具体结果之前，我们对一个随机变量取值的"惊讶"程度的期望值。 ...

Core Viewpoint - The article explores the complex phenomenon of consciousness from various interdisciplinary perspectives, aiming to connect different theories and establish a computational framework for understanding consciousness and its implications for artificial intelligence [2][9]. Group 1: Introduction and Definition of Consciousness - Consciousness is defined as a multifaceted concept involving awareness, wakefulness, and subjective experience, with distinctions made between these related but different concepts [7][16]. - The article emphasizes the importance and difficulty of understanding human consciousness, aiming to engage various research communities in this exploration [7][8]. Group 2: Theoretical Frameworks - The article outlines several influential theories of consciousness, including Information Integration Theory (IIT), Orchestrated Objective Reduction Theory (Orch OR), Global Workspace Theory (GWT), High-Order Theories (HOT), Attention Schema Theory (AST), and Conscious Turing Machine (CTM) [8][38]. - IIT posits that consciousness corresponds to the ability of a system to integrate information, with a focus on the causal power of the system [42][46]. Group 3: Measurement of Consciousness - Recent research has developed effective methods for measuring human consciousness, including indices based on electrical signals and behavioral assessments [18][19]. - The Perturbational Complexity Index (PCI) is highlighted as a significant measure for distinguishing between conscious and unconscious states [19][20]. Group 4: Consciousness and Intelligence - The article discusses the distinction between consciousness and intelligence, noting that consciousness is often considered more mysterious and difficult to measure than intelligence [22][23]. - The relationship between consciousness and free will is explored, with ongoing debates about the existence of true free will and its connection to consciousness [28][29]. Group 5: Sleep and Consciousness - The article examines consciousness during sleep, noting that different sleep stages (REM and NREM) exhibit varying levels of awareness and perception [35][36]. - Information Integration Theory suggests that consciousness diminishes during deep sleep due to reduced integration of brain activity [36][37]. Group 6: Biological Evidence and Theories - The article discusses biological evidence supporting the theories of consciousness, particularly the role of the brain's cortical areas in information integration [49]. - The Orch OR theory is presented as a hypothesis linking consciousness to quantum processes, suggesting that true randomness may be necessary for free will [65].