Information, order, complexity, and entropy in materials including biological systems: a thermodynamic theory based on state variables

Abstract

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.