High Quality Content by WIKIPEDIA articles! In statistical mechanics, a semi-classical derivation of the entropy that doesn`t take into account the indistinguishability of particles, yields an expression for the entropy which is not extensive (is not proportional to the amount of substance in question). This leads to an apparent paradox known as the Gibbs paradox, allowing, for instance, the entropy of closed systems to decrease, violating the second law of thermodynamics. It is possible, however, to take the perspective that it is merely the definition of entropy that is changed to ignore particle permutation (and thereby avert the paradox).