Comparison between two methods for mapping fluctuations in a simulation cell onto a macrovolume

This paper compares two methods for extending the results of simulations of physical clusters (of interest to nucleation theory) to the macrosystem in which the simulation cell is supposed to be immersed. A particular cluster model is studied in which one of the defining parameters is the volume of a “container” to which the cluster molecules are confined. The two mapping processes are conveniently and respectively referred to as the “tiling method” and the “macromethod.” Although the tiling method has been the method of choice in simulations, it is shown to be only approximate, because of a redundant counting of molecular configurations, and it is also shown that the tiling method can be derived if redundancy is ignored. On the other hand, the macromethod is derived when redundancy is properly accounted for. In certain limit situations, the tiling method converges on the macromethod but it still represents an approximation. The issue dealing with redundancy is subtle. We emphasize the fact that, short of a full, direct molecular dynamics simulation, all theories of nucleation require the use of a model. We also present a simple cluster center of mass argument that verifies the “macromethod.” The mapping problem could arise in connection with localized fluctuations beyond those that represent physical clusters.