On a debate over the simulation and mapping of physical clusters in small cells

This paper attempts to resolve some issues in a published debate concerning the types of approximations involved, either implicitly or explicitly, in an innovative method for the simulation of small physical clusters. The method consists of first simulating the probability that a cluster will be found in a small subvolume of a macrovolume, followed by the use of this probability in the evaluation of the equilibrium number of clusters in the macrosystem. Under certain conditions the quantitative accuracy of the method remains high, regardless of the approximations. However, some of the approximations are subtle and impact the fundamental basis of statistical mechanics. Therefore, it is important to understand them as thoroughly as possible.