Zusammenfassung
We consider the Hawking-Page phase transition between the BTZ black hole of
\$M 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 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.
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