Entropy budget for Hawking evaporation

TL;DR

The paper shows that entropy production in blackbody radiation, though linked to coarse-graining, is balanced by hidden correlations due to unitarity, and extends this logic to Hawking evaporation by adopting a tripartite pure-state model that includes the rest of the universe. It derives a consistent entropy budget for Hawking radiation, with a thermodynamic Clausius balance mirroring the Bekenstein entropy flow, and demonstrates that entanglement entropy, analyzed via Page’s framework, can reproduce these results only when environmental degrees of freedom are included. The authors argue that a tripartite (black hole, radiation, environment) approach resolves the information paradox concerns associated with the bipartite Page curve, yielding a continuous purification of radiation and no need for exotic physics such as firewalls. The work highlights the importance of environment in quantum information budgeting for gravitational systems and provides a quantitative bridge between classical thermodynamics and quantum entanglement in black hole evaporation.

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.

Figures (4)

• Figure S1: Clausius (thermodynamic) entropy balance: As the black hole Bekenstein entropy (defined in terms of the area of the horizon) decreases, the Clausius entropy of the radiation increases, to keep total entropy constant and equal to the initial Bekenstein entropy.
• Figure S2: Page curves for entanglement entropy and asymmetric subsystem information: These are derived under the "average subsystem" assumption applied to a pure-state bipartite system consisting only of (black hole) plus the (Hawking radiation).
• Figure S3: Modified Page curves for the bipartite mutual information and the asymmetric subsystem information: These are derived under the "average subsystem" assumption applied to a pure-state bipartite system consisting only of (black hole) plus the (Hawking radiation).
• Figure S4: Tripartite quantum (von Neumann) entropy balance: Under the "average subsystem" assumption, now applied to a pure-state tripartite system consisting of (black hole) plus (Hawking radiation) plus (rest of universe), the quantum (von Neumann) analysis reproduces the Clausius (thermodynamic) analysis. As the black hole Bekenstein entropy decreases, the entanglement entropy of the radiation increases, to keep total entropy approximately constant, at least to within 1 nat. In the limit where the environment (rest of universe) becomes arbitrarily large the correspondence is exact.