A Proof of the Generalized Second Law for Two-Dimensional Black Holes

Abstract

We investigate the generalized second law for two-dimensional black holes in equilibrium (Hartle-Hawking) and nonequilibrium (Unruh) with the heat bath surrounding the black holes. We obtain a simple expression for the change of total entropy in terms of covariant thermodynamic variables, which is valid not only for the Hartle-Hawking state but also for the Unruh state up to leading order, without assuming a quasi-stationary evolution of the black holes. Using this expression, it is shown that the rate of local entropy production is non-negative in the two-dimensional black hole systems.

15 pages, boundary condition of static black hole is added to clarify the situation, abstract and section 4 (concluding remarks) is rewritten, and minor corrections, references added

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