The “Thermodynamics” of the City

The primary objectives of this chapter are twofold: first, to offer a review of progress in urban modelling using the methods of statistical mechanics; and second, to explore the possibility of using the thermodynamic analogy in addition to statistical mechanics. We can take stock of the “thermodynamics of the city” not in the sense of its physical states – interesting though that would be – but in terms of its daily functioning and its evolution over time. We will show that these methods of statistical mechanics and thermodynamics illustrate the contribution of urban modelling to complexity science and form the basis for understanding the evolution of urban structure. It is becoming increasingly recognised that the mathematics underpinning thermodynamics and statistical mechanics have wide applicability. This is manifesting itself in two ways: broadening the range of systems for which these tools are relevant; and seeing that there are new mathematical insights that derive from this branch of Physics. Examples of these broader approaches are provided by Beck and Schlagel (1993) and Ruelle (1978, 2004). The recognition of the power of the method and its wider application goes back at least to the 1950s (Jaynes, 1957, for example) but understanding its role in complexity science is much more recent. However, these methods are now being seen as offering a major contribution. In general, the applications have mainly been in fields closely related to the physical sciences. The purpose of this chapter is to demonstrate the relevance of the methods in a field that has had less publicity but which is obviously important: the development of mathematical models of cities. The urban modelling field can be seen, in its early manifestation, as a precursor of complexity science; and, increasingly, as an important application within it (Wilson 2000).