  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.
