Entropy budget for Hawking evaporation

TL;DR

This paper analyzes the entropy and information budget of Hawking radiation, demonstrating that unitarity ensures a consistent entropy/information accounting during black hole evaporation, similar to blackbody radiation.

Contribution

It extends the entropy/information analysis of blackbody radiation to Hawking radiation, incorporating a tripartite system to account for the universe's influence and black hole entropy.

Findings

Entropy per photon in blackbody radiation is about 3.9 bits.

Unitarity implies a balanced entropy and hidden information in Hawking radiation.

Black holes can have non-zero entropy during evaporation, consistent with Bekenstein entropy.

Abstract

Blackbody radiation, emitted from a furnace and described by a Planck spectrum, contains (on average) an entropy of $3.9\pm 2.5$ bits per photon. Since normal physical burning is a unitary process, this amount of entropy is compensated by the same amount of "hidden information" in correlations between the photons. The importance of this result lies in the posterior extension of this argument to the Hawking radiation from black holes, demonstrating that the assumption of unitarity leads to a perfectly reasonable entropy/information budget for the evaporation process. In order to carry out this calculation we adopt a variant of the "average subsystem" approach, but consider a tripartite pure system that includes the influence of the rest of the universe, and which allows "young" black holes to still have a non-zero entropy; which we identify with the standard Bekenstein entropy.