Clusters as tools to link macro and micro approaches

Physical sciences have two distinct approaches, the macroscopic as exemplified by thermodynamics, and the microscopic, based on the behavior and interactions of individual atoms and molecules. These two have coexisted with virtually no links to join or bridge between them. This paper outlines an approach that achieves one kind of bridge, specifically by offering a way to determine the upper size limit of individual systems that do not conform to the macroscopic description of a chosen property or phenomenon. Despite the random motion of the atoms, extending macroscopic methods to clusters requires additional information because of their size-specific and structure-specific properties.