  The thermodynamic stability of braneworld cosmological solutions in
five-dimensional Einstein-Gauss-Bonnet gravity is addressed, particularly in
the context of the splitting vacuum thin shells in which the shells represent
either an ephemeral or a branch-changing false vacuum bubble spontaneously
emerging from the braneworld and there is more than one possible solution for
the same distributional initial data set. The free energy associated with the
competing solutions is computed. It is shown that the criterion to decide which
solution is preferred coincides with the criterion of the possibility of having
a splitting solution. This result suggests an equivalence between a
thermodynamic and a dynamic selection criteria among possible classical
solutions that deserve further consideration.
