  We study the thermodynamics and the phase structures of Reissner-Nordstrom
and Born-Infeld black holes in AdS space by constructing ``off-shell'' free
energies using thermodynamic quantities derived directly from the action. We
then use these results to propose ``off-shell'' effective potentials for the
respective boundary gauge theories. The saddle points of the potentials
describe all the equilibrium phases of the gauge theories.
