Emergence of space from the first law of thermodynamics in the braneworld scenarios

Expansion of the universe is caused by the departure from the holographic equipartition. This principle, the law of emergence, first postulated in the context of Einstein's gravity has been extended successfully to more general gravity theories like Gauss-Bonnet and Lovelock gravity. We derive the law of emergence for braneworld models of gravity, starting from the more fundamental and well established principle, the first law of thermodynamics. More specifically, we derive the law of emergence in the context of RS II braneworld, Warped DGP model and Gauss-Bonnet braneworld and compare the derived law with the one proposed by Sheykhi for the braneworld models. We further show that the law of emergence leads to the maximization of horizon entropy in all these braneworld models. While the law of emergence effectively implies the maximization of horizon entropy, it could be derived from the first law of thermodynamics. Our results suggest that the horizon thermodynamics is the backbone of the law of emergence in the braneworld scenarios.