Mapping of simulated localized fluctuations onto a macrosystem: Direct counting in the macrosystem to confirm statistical mechanical theory

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Abstract
It has been shown that an appropriate model dependent volume scale is required to map the number of clusters observed in a simulation cell onto the macrovolume. Statistical mechanical theory shows that for overlapping clusters in an ideal gas the volume scale should be kT/(P+Pn). The same volume scale has been predicted for nonoverlapping clusters, but is restricted to only very rare clusters. An alternative theory suggests that the volume scale should be the volume of the cell v̂. In this work we count, by computer simulation, the number of overlapping and nonoverlapping clusters in the macrovolume of a one-dimensional ideal gas. The results confirm that the first volume scale is indeed correct suggesting that its underlying statistical theory should be valid for other models. For nonoverlapping clusters that are not rare the alternative volume scale is a good approximation, however, estimates show that for very rare clusters, such as those used in nucleation, the two volume scales for nonoverlapping clusters differ by up to two orders of magnitude.