Generalized covariant entropy bound in Lanczos-Lovelock gravity

In this paper, we investigate the generalized covariant entropy bound in the theory where the Einstein gravity is perturbed by the higher-order Lovelock terms. After choosing the light sheet that is smooth under the perturbation limit, replacing the Bekenstein-Hawking entropy with the Jacobson-Myers entropy, and introducing two reasonable physical assumptions, we show that the corresponding generalized covariant entropy bound is satisfied under a higher-order approximation of the perturbation from the higher-order Lovelock terms. Our result implies that the Jacobson-Myers entropy strictly obeys the entropy bound under the perturbation level, and the generalized second law of Lanczos-Lovelock gravity is also satisfied when the Einstein gravity is perturbed by the higher-order Lovelock terms.