包括生物系统在内的材料中的信息、序、复杂性与熵：基于状态变量的热力学理论
Information, order, complexity, and entropy in materials including biological systems: a thermodynamic theory based on state variables
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中文总结 AI 辅助
本文针对材料（含生物系统）中熵等概念的歧义问题，提出基于状态变量的热力学理论，以时间平均原子位置为固体状态变量，统一熵等概念并解决与第三定律的矛盾。
中文摘要 AI 辅助
熵在热力学、统计力学、信息论及生物学中均处于核心地位。然而，当将信息论概念应用于包括生物系统在内的材料时，其解释会变得愈发模糊。例如，在生物学中，常见做法是通过枚举DNA的可能构型来评估其熵。这种构型熵在T=0时并未消失，显然与热力学第三定律相矛盾。在将熵与序、随机性、复杂性及信息关联时，也会出现类似的概念性困难。在热力学中，熵是一个状态函数，因此熵必须由材料的给定状态唯一确定。关键问题在于识别能唯一指定材料热力学状态的状态变量。通过建立平衡态与状态变量的一致定义，研究发现时间平均原子位置可作为固体的状态变量。这得出一个重要结论：固体在固定温度和体积下仍拥有众多平衡态。熵并非信息，而是与状态变量相关的不确定性；后者则承载着材料的信息。该框架为熵、信息、序、复杂性、滞后效应及剩余熵提供了统一的热力学基础，同时保留了热力学第三定律。冻结构型及其激活过程解决了热力学熵评估中诸多长期存在的歧义。
英文摘要
Entropy plays a central role in thermodynamics, statistical mechanics, information theory, and biology. However, its interpretation becomes increasingly ambiguous when information-theoretic concepts are applied to materials, including biological systems. For example, in biology, it is common practice to evaluate the entropy of DNA by enumerating possible configurations. This configuration entropy does not vanish at $T=0$, apparently contradicting the third law. Similar conceptual difficulties also arise in relating entropy to order, randomness, complexity, and information. In thermodynamics, entropy is a state function, and hence the entropy must be uniquely determined by a given state of a material. The crucial issue is therefore to identify the state variables that uniquely specify the thermodynamic state of a material. By establishing consistent definition of equilibrium and state variable, it is found that the time-averaged atom positions serve as the state variables of a solid. This leads to the important conclusion that a solid possesses many equilibrium states even at fixed temperature and volume. Entropy is not information but uncertainty associated with the state variables. The latter quantities convey the information of a material. This framework provides a unified thermodynamic basis of entropy, information, order, complexity, hysteresis, and residual entropy while preserving the third law. Frozen configurations and their activation resolve many longstanding ambiguities the thermodynamic evaluation of entropy.
