Alternative derivation of Widom's test particle insertion method using the small system grand canonical ensemble

By using the small system grand canonical ensemble of Soto-Campos, G., Corti, D. S., and Reiss, H., 1998, J. chem. Phys., in press, an alternative derivation is presented of the test particle insertion method for calculating the excess chemical potential of a system of interacting particles. By letting an arbitrarily placed open region within the fluid approach zero volume, the chemical potential is shown to be given by the particle insertion method. The potential benefits of the small system ensemble in obtaining accurate estimates of the chemical potential for dense systems are discussed.