The Widom insertion method is a statistical thermodynamic approach to the calculation of material and mixture properties. It is named for Benjamin Widom, who derived it in 1963. In general, there are two theoretical approaches to determining the statistical mechanical properties of materials. The first is the direct calculation of the overall partition function of the system, which directly yields the system free energy. The second approach, known as the Widom insertion method, instead derives from calculations centering on one molecule. The Widom insertion method directly yields the chemical potential of one component rather than the system free energy. This approach is most widely applied in molecular computer simulations but has also been applied in the development of analytical statistical mechanical models. The Widom insertion method can be understood as an application of the Jarzynski equality since it measures the excess free energy difference via the average work needed to perform, when changing the system from a state with N molecules to a state with N+1 molecules. Therefore it measures the excess chemical potential since μ μ excess = Δ Δ F excess Δ Δ N , where Δ Δ N = 1 .