THERMODYNAMICAL STABILITY OF THE 2-DIMENSIONAL DILATON THEORY OF GRAVITY

In the two-demensional dilaton theory of gravity with dilaton Ricci sc alar curvature coupling, the quasilocal energy, the quasilocal pressur e, and the entropy are calculated by the method given by Creighton and Mann. The heat capacity is also discussed in order to investigate the stability of the thermodynamic system. As a result, by introducing a boundary with a finite radius, we cannot always obtain a thermodynamic ally stable system. This result is opposite to those of the usual two- dimensional thoery without the dilaton Ricci scalar curvature coupling and the four-dimensional Einstein theory, but similar to that of the Liouville theory. This model also respects the third law of thermodyna mics.