x ˙ ˙ ( t ) = − − ∂ ∂ U ( x ( t ) ) + ( 2 Θ Θ ) 1 / 2 ξ ξ ( t ) , where x ∈ ∈ X , ξ ξ ∈ ∈ R n is the noise variable, Θ Θ is the noise intensity, and ∂ ∂ U ( x ) , which in coordinates ( ∂ ∂ U ( x ) ) i ≡ ≡ δ δ i j ∂ ∂ j U ( x ) and ∂ ∂ i U ( x ) ≡ ≡ ∂ ∂ U ( x ) / ∂ ∂ x i , is the gradient flow vector field with U ( x ) being the Langevin function often interpreted as the energy of the purely dissipative stochastic dynamical system.