Langevin equation

Summary

The Langevin equation is a stochastic differential equation for the motion of a particle in a fluid. It combines a deterministic force, a friction force proportional to the velocity, and a random force from collisions with the molecules of the fluid. The friction and the strength of the noise are tied by the temperature, so that the particle reaches thermal equilibrium. Without an external force, the velocity is an Ornstein–Uhlenbeck process.