Spatializing Shannon entropy: a Gaussian Kernel approach to studying the territorial distribution of selected foreign population groups in Italy

The paper proposes an original extension of the Shannon Entropy index that incorporates the spatial dimension in measuring the territorial distribution of population groups. This methodological advancement is achieved through the use of a Gaussian Kernel approach, which enhances the utility of the Shannon Entropy index, particularly for processes that are inherently spatial, such as residential segregation and related phenomena. This spatialized entropy approach contributes theoretically by integrating spatial analysis with information theory, enabling multiscale assessments of spatial structure—an increasingly important objective in contemporary social science research. Compared to standard indices, this method enhances sensitivity to geographic context and facilitates a distance-based assessment that transcends the administrative boundaries of the phenomenon under study. An empirical application is presented, focusing on the spatial distribution of selected foreign groups residing in Italy. The results highlight notable characteristics of the index and suggest steps toward new approaches for measuring the territorial distribution of populations.