(Abstract published in

**Shu-Kun Lin**

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 [1]: _{
}
(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].

[1] S.-K. Lin, *J. Chem. Inf. Comp. Sci.* **1996**, *36*,
367-376.

[2] (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.

[3] Lin, S.-K. *J. Mol. Struct. Theochem* **1997**, *398*,
145-154.