Monte Carlo simulations were one of the first applications running on supercomputers. One therefore may argue that it is very surprising that it took more than 20 years before the first Gibbs ensemble simulation was presented. In particular, as the beauty of the Gibbs ensemble is that it significantly reduces the amount of CPU time needed to compute the vapor-liquid equilibria.

An important side effect of the Gibbs ensemble is that it illustrated that one can use intelligent combinations of Monte Carlo schemes to better mimic the experimental systems. In this respect, one can see that the Gibb ensemble motivated many of us to use the flexibility of the Monte Carlo method to sample phase space with an efficiency that would never be achieved using conventional molecular dynamics simulations. In this lecture this point will be illustrated with some practical applications in the field of Chemical Engineering.