Entransy of Urban Motion: Minimizing Travel Energy Shapes Pedestrian-Bus Districts

Abstract

Mohammad Yaghoub Abdollahzadeh Jamalabadi

The constructal law has been successfully applied to optimize urban district shapes and public transportation routes by minimizing area-averaged travel energy. We introduce a scalar potential field representing the minimum remaining travel cost and a mobility conductivity that is inversely proportional to the specific energy coefficients of walking and bus travel. The total entransy dissipation over the district is shown to be exactly the total travel energy of all residents. Minimizing this dissipation under a fixed area constraint recovers the optimal aspect ratio and bus-line length obtained by constructal theory. Explicit analytical expressions for the entransy dissipation in the three walking zones are derived, and the equivalence between the two principles is demonstrated. The results suggest that EDEP can serve as a unifying variational principle for flow systems ranging from heat conduction to urban traffic.

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