Density-functional fluctuation theory of crowds*

In 2017, in at least 9 separate incidents large crowds transitioned to dangerous stampedes causing hundreds of injuries and 68 deaths. The ability to predict a crowd’s state and whether it is susceptible to such transitions could prevent such catastrophes. We developed, and confirmed in a model system of fruit flies, a quantitative method that uses observations of local density to predict how crowds distribute themselves spatially and simultaneously measure the crowd’s “mood”. Our data-driven approach, inspired by DFT and statistical physics methods, extracts two independent functions to describe the crowd’s behavior. These functions separate individuals’ interactions with each other from interactions with their environment. We use these functions to quantify distinguishable collective behaviors of fruit flies and predict how they will distribute themselves in new environments. We also quantify interactions in multi-component systems to measure the mixing preference between male and female flies. If such techniques extend to human crowds, then observations of sparse crowds could be used to better prepare for highly crowded events and alert when a transition to a stampede is imminent.