  The de Sitter thermodynamics of cosmological models with a modified Friedmann
equation is considered, with particular reference to high-energy
Randall-Sundrum and Gauss-Bonnet braneworlds. The Friedmann equation can be
regarded as the first law of thermodynamics of an effective gravitational
theory in quasi de Sitter spacetime. The associated entropy provides some
selection rules for the range of the parameters of the models, and is proposed
for describing tunneling processes in the class of high-energy gravities under
consideration.
