Landauer’s principle and black hole area quantization

Abstract

This article assesses Landauer’s principle from information theory in the context of area quantization of the Schwarzschild black hole. Within a quantum-mechanical perspective where Hawking evaporation can be interpreted in terms of transitions between the discrete states of the area (or mass) spectrum, we justify that Landauer’s principle holds consistently in the saturated form when the number of microstates of the black hole goes as \(2^n\), where \(n\) is a large positive integer labeling the levels of the area/mass spectrum in the semiclassical regime. This is equivalent to the area spacing \(\Delta A = \alpha l_P^2\) (in natural units), where \(\alpha = 4 \ln 2\) for which the entropy spacing between consecutive levels in Boltzmann units coincides exactly with one bit of information. We also comment on the situation for other values of \(\alpha \) prevalent in the literature.