Statistical mechanics of restroom choice

Human behavior is influenced not only by social interactions but also by the way people interact with their environment. Understanding these different interactions in constrained environments is a central question in behavioral science, but it remains challenging due to the difficulties of data collection. We focus on restrooms with a given number of sites, such as urinals or toilets, as a minimal setting for investigating human behavior. We introduce a web-based platform that enables the collection of large-scale data on sequential occupancy choices in controlled restroom layouts. We analyze transition probabilities between configurations using a statistical physics framework inspired by the Ising model, from which we infer effective interpersonal interactions and site-dependent biases. We further develop a kinetic model describing individual arrivals and departures, which allows us to predict site usage as a function of the utilization factor. Finally, we demonstrate that the model generalizes across restroom of different sizes, enabling prediction of usage and dynamics from limited data. Beyond this specific system, our results demonstrate how simple local rules can generate predictable collective behavior in constrained environments, with implications for a broad class of public spaces such as waiting room or public transportation.