Consider an overdamped Brownian particle under external force F ( r ) : m r ¨ ¨ = − − γ γ r ˙ ˙ + F ( r ) + σ σ ξ ξ ( t ) where the m r ¨ ¨ term is negligible (the meaning of "overdamped"). Thus, it is just γ γ d r = F ( r ) d t + σ σ d W t . The Fokker–Planck equation for this particle is the Smoluchowski diffusion equation: ∂ ∂ t P ( r , t | r 0 , t 0 ) = ∇ ∇ ⋅ ⋅ [ D ( ∇ ∇ − − β β F ( r ) ) P ( r , t | r 0 , t 0 ) ] Where D is the diffusion constant and β β = 1 k B T . The importance of this equation is it allows for both the inclusion of the effect of temperature on the system of particles and a spatially dependent diffusion constant.