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In the context of $\mathcal{N}=4$ SYM, we compute the finite 't Hooftcoupling $\lambda$ correction to the non-linear second-order hydrodynamiccoefficient $\lambda_3$ from a Kubo formula based on fully retarded three-pointfunctions using AdS/CFT. Although $\lambda_3$ is known to vanish in theinfinite 't Hooft coupling limit, we find that the finite $\lambda$ correctionis non-zero. We also present a set of Kubo formulae for the non-linearcoefficients $\lambda_{1,2,3}$, which is more convenient than the one that hasappeared recently elsewhere.

Causal three-point functions and nonlinear second-order hydrodynamic coefficients in AdS/CFT