Mathematics – Probability
Scientific paper
Aug 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994phrvd..50.2373s&link_type=abstract
Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 50, Issue 4, 15 August 1994, pp.R2373-R2375
Mathematics
Probability
1
Quantum Aspects Of Black Holes, Evaporation, Thermodynamics, Multivariate Analysis, Quantum Mechanics, Quantum Ensemble Theory
Scientific paper
The question of whether black holes deplete the Universe of information is usually addressed in terms of initial gravitationally collapsing pure states. Pure states are nongeneric, having null prior probability of occurrence. The more realistic case of initial mixed states is, thus, examined here. The average information in an m-dimensional system in a random mixed state is found to approach asymptotically, as m-->∞, an upper limit of 1/6 nats, that is, 1/6 ln 2 or 0.240449 bits. Also, the average information in an m-dimensional subsystem A of an mn-dimensional system AB proves to be smaller if AB is in a random mixed state than in a random pure state. This finding reinforces the recently drawn conclusion of Page that information in black hole radiation may come out initially so slowly that it would never show up in an analysis perturbative in MPlanck/M.
Slater Paul B.
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