Phys. Rev. Lett. 56, 1885–1888 (1986)Toward a Proof of Entropy Increase in the Presence of Quantum Black HolesReceived 10 February 1986; published in the issue dated 5 May 1986 A sufficient condition for the quantum entropy, -Tr(ρlnρ), to be nondecreasing under a tracepreserving positive linear map is that the "totally random" state, ρ∝1, be stationary. It is argued that this condition will be satisfied by the quantum system consisting of the region external to one or more black holes. This would explain why a "generalized second law of thermodynamics" appears to hold in the presence of black holes. © 1986 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.56.1885
DOI:
10.1103/PhysRevLett.56.1885
PACS:
04.60.+n, 05.30.-d, 97.60.Lf
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