Computer simulations in the Gibbs ensemble

In this article we demonstrate that the Gibbs ensemble and the canonical ensemble are equivalent in the thermodynamic limit. Furthermore, we discuss some interesting aspects of the method when applied close to the critical point. We show that for a finite number of particles the Gibbs ensemble leads to a lower value of the critical temperature of the finite system than that obtained by standard N,V,T simulations with the same number of particles. This is due to entropic considerations. Simulations in the Gibbs ensemble, because it allows for fluctuations in the number of particles and in the volume of the sub-systems, may lead to a better estimate of the critical temperature of the infinite system.