Green-Kubo Relations

Velocity autocorrelation · Fluctuation-dissipation · Diffusion coefficient
Brownian particles (2D)
Velocity Autocorrelation C(τ)
Mean Squared Displacement ⟨Δr²(t)⟩ = 2dDt
20
0.80
0.50
Green-Kubo: D = ∫₀^∞ C(τ)dτ = ∫₀^∞ ⟨v(0)·v(τ)⟩dτ
Einstein: ⟨Δr²(t)⟩ = 2dDt (long times)
FDT: D = k_BT/γ (fluctuation-dissipation)
D (Green-Kubo): — | D (Einstein): — | D (FDT): —