We simulate a 1D chain of N atoms with nearest-neighbor interactions V(r) = ½kr² + (α/3)r³ + (β/4)r⁴ (the Fermi-Pasta-Ulam-β model). Equations of motion are integrated via Störmer-Verlet. The heat flux J = Σᵢ vᵢ · ∂H/∂xᵢ. Running the autocorrelation ⟨J(0)J(t)⟩ and integrating gives a running estimate of κ. The top panel shows atomic displacements; middle shows the instantaneous heat flux; bottom shows the running κ estimate converging.