Information Erasure and the Generalized Second Law of Black Hole Thermodynamics

We consider the generalized second law of black hole thermodynamics in the light of quantum information theory, in particular information erasure and Landauer’s principle (namely, that erasure of information produces at least the equivalent amount of entropy). A small quantum system outside a black hole in the Hartle-Hawking state is studied, and the quantum system comes into thermal equilibrium with the radiation surrounding the black hole. For this scenario, we present a simple proof of the generalized second law based on quantum relative entropy. We then analyze the corresponding information erasure process, and confirm our proof of the generalized second law by applying Landauer’s principle. PACS: 04.70.Dy, 03.67-a. The correspondence between the laws of thermodynamics and black hole mechanics was noted, as a curiosity without physical implications, in a seminal paper by Bardeen, Carter and Hawking [1]. At around the same time, Bekenstein [2] was advocating a rather more radical approach. Noting the area theorem of black holes, which states that the total area of black hole event horizons can never decrease, he observed that this is analogous to the ordinary second law of thermodynamics, i.e. the total entropy of a closed system never decreases. He proposed that, multiplied by appropriate powers of the Planck length, Boltzmann constant and some dimensionless constant of order unity, the black hole area should be interpreted as its physical entropy. This proposal was given physical support by the discovery of Hawking [3] that black holes radiate at a temperature