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

TL;DR

This paper proves the generalized second law of thermodynamics for two-dimensional black holes in both equilibrium and nonequilibrium states by deriving a simple, covariant entropy change expression that confirms non-negative entropy production.

Contribution

It introduces a universal covariant formula for entropy change applicable to different black hole states without assuming quasi-stationarity.

Findings

Entropy production rate is non-negative in two-dimensional black hole systems.

Derived a simple expression for total entropy change valid for both Hartle-Hawking and Unruh states.

Confirmed the generalized second law holds beyond quasi-stationary approximations.

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.