Presented at the New Swiss Chemical Society (NSCS) Fall Meeting, Universite de Lausanne, 15 October 1997.
(Abstract published in Chimia, 1997, 51, 646)

Physical Chemistry, Poster 229

Gibbs Paradox of Entropy of Mixing

Shu-Kun Lin

MDPI Center, Sängergasse 25, CH-4054, Basel (

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.