Cities interact with and rely on energy in complex ways. Fundamentally cities rely upon high quality energy and outputs of low quality for their very existence. The energy flows and transformations enabling cities are tied to physical limits imposed by thermodynamics. Understanding of these limits and the relationships among energy and cities, it is revealed herein, is of vital importance to the sustainability of cities. Four contributions to this understanding are provided. The first articulates how the thermodynamic forces driving cities, together with the dynamic environment within which cities reside, stipulates what type of activities within cities are sustainable. Second, a model depicting the scaling relationship between urban energy use and economic output is devised, and it’s fit to historical data demonstrated via nonlinear regression. By differentiating between energy used to grow and energy used to maintain economic output the model illustrates how reductions in these values on a per dollar basis abets growth while the reverse delays growth, or stops it altogether when energy needs for maintenance become too high. Third, an exergy network conceptualization of cities is developed that reveals the structure of the exergy flows in a city. The topology of the network drastically alters the city’s ability to maximize usefulness of imported energy as well as alter that variability in the amount of usefulness extracted. Finally, the resilience of cities with respect to energy is presented by considering the energy storage and buffer capacity of the urban metabolism. The city of Toronto is shown to have adequate flexibility in food and transport fuels to withstand operation for days without undue interruption of typical activities. Together these differing aspects of the open non-equilibrium details of cities establish an improved prescription of the sustainable city.

Cities interact with and rely on energy in complex ways. Fundamentally cities rely upon high quality energy and outputs of low quality for their very existence. The energy flows and transformations enabling cities are tied to physical limits imposed by thermodynamics. Understanding of these limits and the relationships among energy and cities, it is revealed herein, is of vital importance to the sustainability of cities. Four contributions to this understanding are provided. The first articulates how the thermodynamic forces driving cities, together with the dynamic environment within which cities reside, stipulates what type of activities within cities are sustainable. Second, a model depicting the scaling relationship between urban energy use and economic output is devised, and it’s fit to historical data demonstrated via nonlinear regression. By differentiating between energy used to grow and energy used to maintain economic output the model illustrates how reductions in these values on a per dollar basis abets growth while the reverse delays growth, or stops it altogether when energy needs for maintenance become too high. Third, an exergy network conceptualization of cities is developed that reveals the structure of the exergy flows in a city. The topology of the network drastically alters the city’s ability to maximize usefulness of imported energy as well as alter that variability in the amount of usefulness extracted. Finally, the resilience of cities with respect to energy is presented by considering the energy storage and buffer capacity of the urban metabolism. The city of Toronto is shown to have adequate flexibility in food and transport fuels to withstand operation for days without undue interruption of typical activities. Together these differing aspects of the open non-equilibrium details of cities establish an improved prescription of the sustainable city.