For a system of N particles with masses M , with coordinates X = X ( t ) that constitute a time-dependent random variable, the resulting Langevin equation is M X ¨ ¨ = − − ∇ ∇ U ( X ) − − γ γ M X ˙ ˙ + 2 M γ γ k B T R ( t ) , where U ( X ) is the particle interaction potential; ∇ ∇ is the gradient operator such that − − ∇ ∇ U ( X ) is the force calculated from the particle interaction potentials; the dot is a time derivative such that X ˙ ˙ is the velocity and X ¨ ¨ is the acceleration; γ γ is the damping constant (units of reciprocal time), also known as the collision frequency; T is the temperature, k B is the Boltzmann constant ; and R ( t ) is a delta-correlated stationary Gaussian process with zero-mean, satisfying ⟨ R ( t ) ⟩ = 0 ⟨ R ( t ) ⋅ ⋅ R ( t ′ ) ⟩ = δ δ ( t − − t ′ )