If the external potential is conservative and the noise term derives from a reservoir in thermal equilibrium, then the long-time solution to the Langevin equation must reduce to the Boltzmann distribution, which is the probability distribution function for particles in thermal equilibrium. In the special case of overdamped dynamics, the inertia of the particle is negligible in comparison to the damping force, and the trajectory x ( t ) is described by the overdamped Langevin equation