In this article, we discuss the application of information theory and the theory of thermodynamic dissipative systems to smart cities. Specifically, we study how to model the interaction between a society and a smart city, under an information-theoretic approach. Because the smart city comprises both a social and a technological component, it then becomes possible to use information theory to study them both. In this paper, we discuss a model that applies the constraints from thermodynamic dissipative systems theory in order to study smart cities, and their associated social system, in their information processing capacity and in their evolution over time. Within the context of our model, we are allowed to study under what conditions a smart city would expand or contract, or to state that the smart city shrinks if its output greatly exceeds its input.