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Maximum-entropy approach to the 1D Traffic Cellular Automata behavior
##manager.scheduler.building##: Edificio Santa Maria
##manager.scheduler.room##: Auditorio San Agustin
Date: 2019-07-08 11:45 AM – 03:30 PM
Last modified: 2019-06-15
Abstract
In this work we show that an entropy function can be defined for the 1D traffic cellular automata in a single line with no anticipation, such as that in the Fukui-Ishibashi (FI) model [Salcido et al, Physica A 494: 276-287, 2018]. By obtaining the exact analytical solution corresponding to the maximum entropy state, we show that it may be useful since it leads to an alternative derivation of general characteristics of particular CA models, such as the partial particle densities and the expression for the average speed in the FI model. Other properties, such as the average flow and average kinetic energy per site can be calculated directly from the partial densities of the system. To test our theoretical results, computer simulations were carried out with the FI traffic model. We found a very good agreement between the steady-state low-density conditions of the simulation results and the analytical expressions obtained from the maximum entropy solution if the system possible microstates are restricted to those where there are only particles with the two highest velocities. It was also shown using different computer simulations of the FI model that, under initial conditions where the mentioned restriction is satisfied, the system entropy per site increases with time, as predicted by the theory.