The Fokker–Planck equation for an underdamped Brownian particle is called the Klein–Kramers equation. If the Langevin equations are written as r ˙ ˙ = p m p ˙ ˙ = − − ξ ξ p − − ∇ ∇ V ( r ) + 2 m ξ ξ k B T η η ( t ) , ⟨ ⟨ η η T ( t ) η η ( t ′ ) ⟩ ⟩ = I δ δ ( t − − t ′ ) where p is the momentum, then the corresponding Fokker–Planck equation is ∂ ∂ f ∂ ∂ t + 1 m p ⋅ ⋅ ∇ ∇ r f = ξ ξ ∇ ∇ p ⋅ ⋅ ( p f ) + ∇ ∇ p ⋅ ⋅ ( ∇ ∇ V ( r ) f ) + m ξ ξ k B T ∇ ∇ p 2 f Here ∇ ∇ r and ∇ ∇ p are the gradient operator with respect to r and p, and ∇ ∇ p 2 is the Laplacian with respect to p.