(Abstract published in

Physical Chemistry, **Poster 229**

__Shu-Kun Lin__

MDPI Center, Sängergasse 25, CH-4054, Basel (Lin@mdpi.org)

Gibbs paradox says that entropy of mixing *decreases* discontinuously with
the increase in molecular similarity. It also implies that entropy (*S*)
of a system *decreases* with the increase in its symmetry, or _{
}
(_{
}:
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. A large number of chemical and physical
observations have been presented to show that the Gibbs paradox of mixing is
itself wrong [1]. It is shown here that the Gibbs paradox statement is false.
We disprove it firstly through the entropy additivity principle, Secondly, from
group theory, any system has a symmetry number _{
}
(_{
}
for the identity operation of a strictly asymmetric system). It follows that
the entropy of any system is equal to, or less than, zero, following the Gibbs
paradox statement. This violates the definition of entropy which is
non-negative. Thirdly, Gibbs's statement of entropy and similarity obviously
violates the inequality _{
}.
In conclusion, _{
}
defines a similarity index, and entropy *increases* continuously with the
property similarity of the *w* microstates or *w* subsystems. Entropy
also *increases* with the symmetry [2]: _{
}
(_{
}:
the apparent symmetry number). The theoretical consequences in chemistry will
be discussed.

[1] S.-K. Lin, *J. Chem. Inf. Comp. Sci.* **1996**, *36*, 367-376.
S.-K. Lin, *J. Theor. Chem.* **1996**, *1*, 135-150.

[2] S.-K. Lin, *Symmetry breaking problem resolved*. Paper presented at
the American Physical Society 1997 March Meeting, Kansas City, MO, March 17-21,
1997.