Entropy production of selfish drivers: Implications for efficiency and predictability of movements in a city

TL;DR

This paper investigates how selfish drivers' movements in cities affect efficiency and unpredictability, revealing that shared information improves predictability and that entropy production can distinguish congestion phases.

Contribution

It introduces a model linking entropy production to city mobility efficiency, showing how randomness and information sharing influence predictability and congestion.

Findings

Shared travel time information enhances predictability.

Larger cities tend to have lower efficiency.

Entropy production differentiates congestion phases.

Abstract

Characterizing the efficiency of movements is important for a better management of the cities. More specifically, the connection between the efficiency and uncertainty (entropy) production of a transport process is not established yet. In this study, we consider the movements of selfish drivers from their homes (origins) to work places (destinations) to see how interactions and randomness in the movements affect a measure of efficiency and entropy production (uncertainty in the destination time intervals) in this process. We employ realistic models of population distributions and mobility laws to simulate the movement process, where interactions are modelled by dependence of the local travel times on the local flows. We observe that some level of information (the travel times) sharing enhances a measure of predictability in the process without any coordination. Moreover, the larger cities display smaller efficiencies, for the same model parameters and population density, which limits the size of an efficient city. We find that entropy production is a good order parameter to distinguish the low- and high-congestion phases. In the former phase, the entropy production grows monotonically with the probability of random moves, whereas it displays a minimum in the congested phase; that is randomness in the movements can reduce the uncertainty in the destination time intervals. The findings highlight the role of entropy production in the study of efficiency and predictability of similar processes in a complex system like the city.