Black hole entropy production and transport coefficients in Lovelock gravity

We study the entropy evolution of black holes in Lovelock gravity by formulating a thermodynamic generalization of the null Raychaudhuri equation. We show that the similarity between the expressions of entropy change of the black hole horizon, due to perturbation, and that of a fluid, which is out of equilibrium, transcends beyond general relativity to the Lovelock class of theories. Exploiting this analogy we find that the shear and bulk viscosities for the black holes in Lovelock theories exactly match with those obtained in the membrane paradigm and also from holographic considerations.