  The Gibbs paradox of the first kind (GP1) refers to the false increase in
entropy which, in statistical mechanics, is calculated from the process of
combining two gas systems S1 and S2 consisting of distinguishable particles.
Presented in a somewhat modified form, the GP1 manifests as a contradiction to
the second law of thermodynamics. Contrary to popular belief, this
contradiction affects not only classical but also quantum statistical
mechanics. The present paper resolves the GP1 by considering two effects: 1.
The uncertainty about which particles are located in S1 and which in S2
contributes to the entropies of S1 and S2. 2. S1 and S2 are correlated by the
fact that if a certain particle is located in one system, it cannot be located
in the other. As a consequence, the entropy of the total system consisting of
S1 and S2 is not the sum of the entropies of S1 and S2.
