Thermodynamics of a gas of pedestrians: theory and experiment

Abstract

In this paper, we perform an experiment on the interaction of pedestrians in a chaotic environment and investigate the possibility to study its results using a thermodynamic model. In contrast to simple single-file unidirectional scenarios, where only distance and time are relevant to adjust walking speed, bidirectional cases are much more complex since pedestrians can perform evading manoeuvres to avoid collisions. To better understand collision avoidance in a bidimensional environment we designed a set of experiments where people need to move chaotically for the whole time. Trajectories of moving pedestrians were obtained by tracking their head position, but a method to obtain body orientation failed, thus limiting reliable information on average quantities, i.e. average density and speed. By analysing those data, we showed that equations for thermodynamic processes can be used to describe pedestrian dynamics from medium densities or a state where interaction distances are very small. To allow combining low density cognitive aspects of collision avoidance with semi-random motion at medium densities we also developed a microscopic simulation model inspired by physics. Results show that, after calibrations, the simulation model allows to reproduce the fundamental diagram of different studies despite the very simple rules implemented. This shows that describing the statistical nature of specific crowds requires a relatively small set of rules and research should focus on cognitive/psychological aspects which are essential for understanding crowds of people.