The Langevin equations for a system in which each particle is affected by an external force formula_81 and also random collisions with other particles must reproduce the Boltzmann distribution, which is the probability distribution function for particles in thermal equilibrium. One-dimensional overdamped This is Brownian motion in the presence of an external forcing. The overdamped case is realized when the inertia of the particle is negligible in comparison to the damping force. The trajectory formula_82 of the particle in a potential formula_83 is described by the Langevin equation