Entropy Conservation in the Transition of Schwarzschild-de Sitter Space to de Sitter Space through Tunneling

We revisit Parikh–Wilczek tunneling through the de Sitter horizon and obtain the tunneling rate in Schwarzschild-de Sitter space, which is non-thermal and closely related to the change of entropy. We discuss the thermodynamics of Schwarzschild-de Sitter space and show existence of correlation which can ensure conservation of the total entropy in the transition process of Schwarzschild-de Sitter space to de Sitter space. The correlation and the conserved entropy provide a way to explain the entropy in empty de Sitter space.