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We derive the effective equations of the membranes dual to black holes in aparticular theory of higher derivative gravity namely Einstein-Gauss-Bonnet(EGB) gravity at sub-leading order in $1/D$ upto linear order in theGauss-Bonnet (GB) parameter $\beta$. We find an expression for an entropycurrent which satisfies a local version of second law onshell in this regime.We also derive the membrane equations upto leading order in $1/D$ butnon-perturbatively in $\beta$ for EGB gravity. In this regime we write down anexpression for a world-volume stress tensor of the membrane and also work outthe effective membrane equation for stationary black holes.

Large D membrane for Higher Derivative Gravity and Black Hole Second Law