Bridging the macro and micro

A long-standing but rarely addressed challenge to physical sciences is reconciling or bridging between the macroscopic approach, exemplified by thermodynamics, continuum and infinite models, and the microscopic approach built from individual elements. Here, we show an approach to finding the boundary size region below which a microscopic approach is mandatory, and above which, one can use the macroscopic approach’s tools. We illustrate how to estimate this boundary size using examples from atomic clusters. The first reviews the boundary size above which the Gibbs Phase Rule is valid, but below, is inapplicable. Then we show how to find boundary sizes for other properties.