Statistical mechanics of colloids and Boltzmann’s definition of the entropy

The Boltzmann entropy as traditionally presented in statistical mechanics textbooks is only a special case and not Boltzmann's fundamental definition. The difference becomes important when the traditional expression for the entropy is applied to colloids, for which it makes incorrect predictions. Boltzmann's original definition of the entropy in terms of the probabilities of states of composite systems leads to consistent and correct statistical mechanics and thermodynamics.