  The traditional approach to the quantitative study of segregation is to
employ indices that are selected by ``desirable properties''. Here, we detail
how information theory underpins entropy-based indices and demonstrate how
desirable properties can be used to systematically construct models of
segregation. The resulting models capture all indices which satisfy the
selected properties and provide new insights, such as how the entropy index
presumes a particular form of intergroup interactions and how the dissimilarity
index depends on the regional composition. Additionally, our approach reveals
that functions, rather than indices, tend to be necessary mathematical tools
for a comprehensive quantification of segregation. We then proceed with
exploratory considerations of two-group residential segregation, finding
striking similarities in major U.S. cities, subtle segregation patterns that
correlate with minority group diversity, and substantive reductions in
segregation that may be overlooked with traditional approaches. Finally, we
explore the promise of our approach for segregation forecasting.
