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We compute the energy diffusion constant $D$, Lyapunov time $\tau_{\text{L}}$and butterfly velocity $v_{\text{B}}$ in an inhomogeneous chain of coupledMajorana Sachdev-Ye-Kitaev (SYK) models in the large $N$ and strong couplinglimit. We find $D\le v_{\text{B}}^2 \tau_{\text{L}}$ from a combination ofanalytical and numerical approaches. Our example necessitates the sharpening ofpostulated transport bounds based on quantum chaos.

Energy diffusion and the butterfly effect in inhomogeneous Sachdev-Ye-Kitaev chains