Entropy and the City: Origins, trajectories and explorations of the concept in urban science

Entropy is arguably one of the most powerful concepts to understand the world, from the behavior of molecules to the expansion of the universe, from how life emerges to how hybrid complex systems like cities come into being and continue existing. Yet, despite its widespread application, it is also one of the most misunderstood concepts across the sciences. This chapter seeks to demystify entropy and its main interpretations, along with some of its explorations in the context of cities. It first establishes the foundations of the concept by describing its trajectory since its inception in thermodynamics and statistical mechanics in the 19th century, its different incarnations from Boltzmanns pioneering formulation and Shannons information theory to its absorption in biology and the social sciences, until it reaches a nascent urban science in the 1960s. The chapter then identifies some of the main domains in which entropy has been explored to understand cities as complex systems, from entropy-maximizing models of spatial interaction and applications as a measure of urban form, diversity, and complexity to a tool for understanding conditions of self-organization and urban sustainability.