Molecular Diversity Preservation International (MDPI)
Sängergasse 25, CH-4054 Basel, Switzerland (Lin@mdpi.org)
Statistical mechanics is the foundation of thermodynamics. Information theory is regarded as the foundation of statistical mechanics. However, it might be a surprise that information theory has never been practically used to the thermodynamic or statistical mechanics problems in chemistry so far. Structural stability and process spontaneity have been characterized by entropy (information loss).
According to Gibbs, entropy of mixing decreases discontinuously with the increase in molecular or quantum state similarity. It also implies that entropy (S) of a system decreases with the increase in its symmetry, or (w: the symmetry number, e.g., the permutation symmetry number N! of an ideal gas of N particles). It is assumed that these relations of entropy are applicable to the formation of a solid, liquid, or gaseous mixture and to the mixing of quantum states involved in all kinds of chemical processes.
A large number of chemical and physical observations have been presented to show that the Gibbs statement of mixing is itself wrong [1,2a]. The Gibbs statement is proved [2a] to be false by considering the entropy additivity principle, the basic principle of group theory, and the inequality . Finally, (where is the probability) defines a similarity index [2b]. Entropy increases continuously with the property similarity of the w microstates or the subsystems. Entropy also increases with the symmetry : (where is the apparent symmetry number). The new information theory [1-2] is applicable to chemical process problems of mixing, self-organization, chemical bonding and deformation [2a,3].
 S.-K. Lin, J. Chem. Inf. Comp. Sci. 1996, 36, 367-376.
 (a) S.-K. Lin, J. Theor. Chem. 1996, 1, 135-150. (b) S.-K. Lin, Molecules 1996, 1, 57-67. These two papers are downloadable from http://www.mdpi.org/lin.htm.
 Lin, S.-K. J. Mol. Struct. Theochem 1997, 398, 145-154.