Statistical Mechanics of Residential Segregation*

Few problems are more complex than those concerned with human systems. Humans make decisions based on historical trends and whims, may be entirely idiosyncratic, and cannot be trusted to provide honest justification for their decisions. Residential segregation is an excellent illustration of such a problem that is of historical importance and continual equity concern, yet one which can be addressed due to the myriad of publicly available data.  Here we demonstrate how traditional demographic approaches, which aim to measure the amount of segregation, are encompassed in statistical mechanics. Furthermore, inspired by density-functional theory, we quantify coarse-grained interactions among various racial/ethnic groups from neighborhood compositions taken at a particular instant in time. These interactions can be used to both generalize traditional demographic approaches, allowing the capture of segregation behavior, while also generating novel neighborhood-level forecasts of racial/ethnic compositions.