Entropy Budget for Hawking Evaporation

Abstract

Blackbody radiation, emitted from a furnace and described by a Planck spectrum, contains (on average) an entropy of 3.9 ± 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.

Generalized uncertainty principle impact onto the black holes information flux and the sparsity of Hawking radiation

“…This reasoning was then extended to the black hole evaporation process, determining the flux of entropy/information emitted in the form of radiation (assuming an exact Planck spectrum as first approximation) [18,19]. For the case of a Schwarzschild black hole with mass M , the Bekenstein entropy loss per emitted massless boson was found to be equal to the entropy content per photon in black body radiation.…”

“…For the case of a Schwarzschild black hole with mass M , the Bekenstein entropy loss per emitted massless boson was found to be equal to the entropy content per photon in black body radiation. In addition, after calculating the gain of entropy in the Hawking flux, one finds that all the information emitted by a black hole is perfectly compensated by the entropy gain of the radiation, so that the information is completely transmitted from the hole to the external radiation [18,19].…”

“…Recently in [17][18][19][20], one of the authors of this paper, quantified the information budget in black hole evaporation. The starting point was the calculation of the budget of entropy for a black body, where the entropy flux is compensated by hidden information in the correlations, due to the emission process is unitary.…”

“…II we review the key results about the information content of black holes as given in Refs. ( [17][18][19][20]). In Sec.…”

Entropy evolution of moving mirrors and the information loss problem

“…2) [31]. In terms of the entanglement entropy, after the mirror stops to move (i.e.,ẋ = 0), it becomes zero again and hence we can regard that information is transmitted from the mirror M to the future infinity by radiation R.…”