The average of this derivative over a duration of time, τ, is defined as ⟨ d G d t ⟩ τ τ = 1 τ τ ∫ ∫ 0 τ τ d G d t d t = 1 τ τ ∫ ∫ G ( 0 ) G ( τ τ ) d G = G ( τ τ ) − − G ( 0 ) τ τ , from which we obtain the exact equation ⟨ d G d t ⟩ τ τ = 2 ⟨ T ⟩ τ τ + ∑ ∑ k = 1 N ⟨ F k ⋅ ⋅ r k ⟩ τ τ .