A Proposal for an Entropy Based Approach to Data Driven Models for Urban Mobility

In this paper we discuss the problem of applying the Maximum Entropy Principle to Markov systems to infer the transition rates using information on the stationary state. We use the Perry's theorem to maximize the dynamical entropy and we generalize the results to Markov systems that express non equilibrium stationary states using the Minimum Entropy Production Principle. We apply these results to a class of non-linear random walk models that simulate the urban mobility on transport network. The main goal is to define data driven simple models that can highlight the interplay between the geometric features of the transport network and the traffic load distribution, in the formation of local congestion and its spreading in the network. Our approach proposes a roadmap to define predictive stochastic models for the congestion formation, using data that can be available in any city. In this way one can addresses the questions if these data contains enough information to set up a predictive model without further assumptions, and if Markov models for urban mobility are suitable to study congestion formation simplifying the great complexity of agent based models. We refer explicitly to the city of Bologna in Italy where a digital twin project for the urban mobility is being developed.