Averaging over all particles yields ⟨∆v2⟩(t) = γ2v2 0τa π Z ∞ −∞ Bv(ω) 2[1−cos(ωt)] 1 +ω 2τ 2a dω,(11) whereB v(ω) encodes the frequency-dependent response of the chain

Mean-squared change in velocity We characterize the velocity dynamics through the mean-squared change in velocity (MSCV), defined as Cv l,m(t) =⟨[v l(t)−v l(0)][vm(t)−v m(0)]⟩, whi