ABSTRACT
The micro-canonical ensemble requires the system to be isolated so that no energy flows in or out of the system. The difference with the corresponding isothermal ensemble is thus that, in the case of the microcanonical ensemble, a thermally insulating boundary needs to surround the system to avoid any heat flow and allow the system to be in thermal equilibrium with the outside world and thus be at the same temperature. Chemical equilibrium arises thanks to the ability of the system to have its density fluctuate through variations. Monte Carlo simulations in the grand-canonical ensembles are a direct route to evaluate the properties of a system in equilibrium with another phase. Monte Carlo simulations in the grand-canonical ensemble are especially appealing since they allow one to calculate ensemble averages without ever determining the value of the grand partition function. Systems in nature rarely contain a single component.
