The three-pillar conception of (social, economic and environmental) sustainability, commonly represented by three intersecting circles with overall sustainability at the centre, has become ubiquitous. With a view of identifying the genesis and theoretical foundations of this conception, this paper reviews and discusses relevant historical sustainability literature. From this we find that there is no single point of origin of this three-pillar conception, but rather a gradual emergence from various critiques in the early academic literature of the economic status quo from both social and ecological perspectives on the one hand, and the quest to reconcile economic growth as a solution to social and ecological problems on the part of the United Nations on the other. The popular three circles diagram appears to have been first presented by Barbier (Environ Conserv 14:101,

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.

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A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription. For the Random Sequential Adsorption model, we introduce the 'availability' as a new variable corresponding to the number of available locations in which an adsorbate can be accommodated. We investigate the relation of the availability to the coverage of the adsorbent surface over time. Power law scaling between the two is obtained both through numerical simulations and analytical techniques for both one and two dimensional RSA, as well as in the case of competitive random sequential adsorption in one dimension.

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