Entropy and its Relation with the Property of Molecule, Phase and Component

We study the relationship of entropy with the properties of molecules and also with the macroscopic specifications of the system, i.e., component and phase. Understanding different viewpoints of classical mechanics and quantum mechanics for the indistinguishability of molecules belonging to the same component, we discuss a few thermodynamic systems in which the properties of molecules are to be consistent with the component as a macroscopic term of classifying the molecules. With a clear definition of thermodynamic microstate, the drawback of the Boltzmann statistics caused by the distinguishability of molecules is avoided, and the Gibbs paradox of entropy consequently disappears. Corresponding to the characteristics of fluid and solid phases, we investigated the effects of the indistinguishability and the symmetry number of molecules and the number of microstates realized in time on the partition function and the entropy. In particular, we show that crystalline solid can be regarded as a system which does not satisfy the ergodic hypothesis.