The overdamped Langevin equation d x t = − − 1 k B T ( ∇ ∇ x U ) d t + d W t gives ∂ ∂ t p = 1 2 ∇ ∇ ⋅ ⋅ ( p k B T ∇ ∇ U + ∇ ∇ p ) . The Boltzmann distribution p ( x ) ∝ ∝ e − − U ( x ) / k B T is an equilibrium distribution, and assuming U grows sufficiently rapidly (that is, the potential well is deep enough to confine the particle), the Boltzmann distribution is the unique equilibrium.