Deep connection between thermodynamics and gravity in Gauss-Bonnet braneworlds

We disclose a deep connection between thermodynamics and gravity in a general braneworld model with curvature correction terms on the brane and in the bulk, respectively. We show that the Friedmann equations on the 3-brane embedded in the 5D spacetime with curvature correction terms can be written directly in the form of the first law of thermodynamics on the apparent horizon. Using the first law, we extract the entropy expression of the apparent horizon on the brane, which is useful in studying the thermodynamical properties of the black hole horizon on the brane in Gauss-Bonnet gravity.