(Abstract published in

**Shu-Kun Lin**

Molecular Diversity Preservation International (MDPI)

Saengergasse 25,
CH-4054 Basel, Switzerland (email: Lin@mdpi.org)

The relations of the two most important concepts, entropy and symmetry, are
mathematically clarified. It has been a tacit assumption that higher symmetry
of a system imply less entropy. However, it is proved here that the opposite is
true for both dynamic and static systems. Higher value of entropy of any system
is correlated to higher symmetry. Entropy (*S*) of a system of *w*
microstates is expressed as a logarithmic function of symmetry,

_{
}

The apparent symmetry number is

_{
}

_{}where _{
}
is the probability of the *i*th microstate.

This relation is broadly useful for solving problems of relative structural stability of both dynamic systems and static structures [1-4].

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

[2] S.-K. Lin, *J. Theor. Chem.* **1996**, *1*, 135-150. This
paper is downloadable from http://www.mdpi.org/lin.htm.

[3] (a) S.-K. Lin, *Understanding structural stability and process
spontaneity based on the rejection of the Gibbs paradox of entropy of
mixing*. Paper presented at the Fourth World Congress of Theoretically
Oriented Chemists, Jerusalem, Israel, July 7-12, 1996.

(b) S.-K. Lin, *J. Mol. Struct. Theochem* **1997**, *398*,
145-154.

[4] S.-K. Lin, *Symmetry-breaking problem resolved*. Paper accepted for
presentation at the American Physical Society 1997 March Meeting, Kansas City,
MO, March 17-21, 1997. Abstract downloadable from
http://www.aps.org/BAPSMAR97/abs/S4580004.html.