Multipartite analysis of average-subsystem entropies

Abstract

Blackbody radiation contains (on average) an entropy of 3.9 ± 2.5 bits per photon. If the emission process is unitary, then this entropy is exactly compensated by "hidden information" in the correlations. We extend this argument to the Hawking radiation from GR black holes, demonstrating that the assumption of unitarity leads to a perfectly reasonable entropy/information budget. The key technical aspect of our calculation is a variant of the "average subsystem" approach developed by Page, which we extend beyond bipartite pure systems, to a tripartite pure system that considers the influence of the environment.

Entropy/information flux in Hawking radiation

“…This is not making any assumptions concerning the actual thermodynamic entropy of the rest of the universe. Under these conditions we have demonstrated (at all times) [58]…”

“…But n H ≤ n R n E , while n R ≤ n H n E , and n H n R ≤ n E . So in dimensionless units, and using the harmonic numbers H n we have the exact result [58] Î H:…”

Extended uncertainty principle for rindler and cosmological horizons

“…In fact, the HUP does neither take into account quantum gravity effects of the photon interaction nor the curvature of space-time. However, widely spread by the considerations of superstring theory [1][2][3][4][5] and loop quantum gravity [6,7], these two phenomena have been gradually taken into account resulting in the Generalised Uncertainty Principle (GUP) [8][9][10][11][12][13][14][15][16][17][18] and the Extended Uncertainty Principle (EUP) [19][20][21][22], or were even put together as the Generalised Extended Uncertainty Principle (GEUP) [23][24][25][26][27]. Yet, a different approach to the problem using the so-called qmetric was also considered [28].…”

“…There have been some attempts to bound the GUP parameter α 0 in (3) observationally [38][39][40][41][42] including the issue of its positivity or negativity [14,[38][39][40][43][44][45][46]. In fact, the microcanonical corrections reduce the entropy and so the parameter α 0 seems to be negative while for the canonical corrections it should be positive [17,23,44]. It is also worth mentioning that there is some analogy between the GUP in particle physics and the solid state phenomena in graphene which could pave the path to experimentally support this idea [47].…”

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

“…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.…”