Entropy and its Application to Urban Systems

Abstract

Since its conception over 150 years ago, entropy has enlightened and confused scholars and students alike, from its origins in physics and beyond. More recently, it has been considered within the urban context in a rather eclectic range of applications. The entropy maximization approach, as applied by Alan Wilson and others from the 1960s, contrasts with considerations from the 1990s of the city as a thermodynamic dissipative system, in the tradition of Ilya Prigogine. By reviewing the relevant mathematical theory, we draw the distinction among three interrelated definitions of entropy, the thermodynamic, the figurative, and the information statistical. The applications of these definitions to urban systems within the literature are explored, and the conflation of the thermodynamic and figurative interpretations are disentangled. We close this paper with an outlook on future uses of entropy in urban systems analysis.

Keywords: cities; dissipative systems; entropy maximisation; information; probability; second law; statistical physics; thermodynamics; urban modeling.