Landauer's principle and black hole area quantization

TL;DR

This paper explores the application of Landauer's principle to the quantized area spectrum of Schwarzschild black holes, linking information theory with quantum gravity and black hole thermodynamics.

Contribution

It demonstrates that Landauer's principle is consistent with black hole area quantization when the microstates follow a specific exponential distribution, connecting entropy, information, and quantum spectra.

Findings

Landauer's principle holds for black holes with microstates proportional to 2^n.

The area spacing corresponds to one bit of information per quantum level.

Entropy spacing matches the Boltzmann units for a specific area quantum.

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.