Assessing the impact of major historical events on urban landscapes via local entropy measures

In this paper we show how Shannon entropy, an intuitive and versatile measure of uniformity of a probability distribution, can be adapted to quantify the heterogeneity of land use and population density in and around human settlements. Using a raster data set of estimates of historical population density and land use, we show that local entropy measures capture salient aspects of the evolution of urban systems. Through the case studies of the UK, India, and Italy we reconnect the temporal evolution of the measures to some of the main socioeconomic and political changes and epidemic events these countries went through during the last three centuries. We argue that the diffusion of technological innovations is more apparently correlated to changes in the measures than epidemic events in themselves. We discuss the potential significance and limitations of this finding in understanding changes in urban systems in the context of the ongoing COVID-19 pandemic.