  We consider the Hawking-Page phase transition between the BTZ black hole of
$M \ge 0$ and the thermal soliton of $M=-1$. In this system, there exists a
mass gap so that there does not seem to exist a continuous thermodynamic phase
transition. We consistently construct the off-shell free energies of the black
hole and the soliton by properly taking into account the conical space. And
then, the continuous off-shell free energy to describe tunneling effect can be
realized through non-equilibrium solitons.
