Краткий обзор статьи: We study quasi-stationary physical process for black holes within the context of Lanczos-Lovelock gravity We show that the Wald entropy of stationary black holes in Lanczos-Lovelock gravity monotonically increases for quasi-stationary physical processes in which the horizon is perturbed by the accretion of positive energy matter and the black hole ultimately settles down to a stationary state