Langevin dynamics is a stochastic differential equation framework that models the motion of particles by combining deterministic forces — such as self-propulsion, interaction potentials, or alignment rules — with stochastic noise terms representing thermal or behavioral fluctuations. In the context of crowd and active matter research, it provides the mathematical backbone for simulating active Brownian particles and cognitive agents, capturing both the directed motion and the inherent randomness of individual pedestrian or particle trajectories. Key variants include overdamped Langevin equations, which neglect inertial effects and are standard for slow-moving or highly damped agents, and underdamped formulations that retain momentum, with extensions such as active Brownian particle models incorporating self-propulsion and intelligent or cognitive variants that additionally encode perception and decision-making rules to reflect the goal-directed behavior of pedestrians.
Dictionary term