This paper considers the roles of the concepts of entropy and complexity in the modeling of urban and regional systems over time. Drawing on Rosser (2016), the concept of entropy will be reviewed from its nineteenth century as the Second Law of Thermodynamics development for statistical mechanics applications through the twentieth century information entropy to more generalized forms. The seminal application to urban and regional economics is due to Wilson (1970) who showed how minimizing transport costs in a market flow model obeys an entropic formulation. Besides this influential model, entropy has been used in studies of spatial settlement distribution, spatial concentration and dispersion, urban sprawl, racial segregation, land use diversity, and measures of sustainability of energy use in urban and regional systems. These entropic forces compete with anti-entropic tendencies associated with agglomeration economies that are associated with the emergence of a power law distribution of the urban hierarchy, with these possibly following Zipf rank-size rule, a matter of long debate. The interaction of these dynamic processes underlies complex dynamics that generate a self-organizing pattern of urban and regional development.
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