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# Time Dependence of Hawking Radiation Entropy

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### Most cited references43

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### Quantum source of entropy for black holes

(1986)
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### The Stretched Horizon and Black Hole Complementarity

(1993)
Three postulates asserting the validity of conventional quantum theory, semi-classical general relativity and the statistical basis for thermodynamics are introduced as a foundation for the study of black hole evolution. We explain how these postulates may be implemented in a stretched horizon'' or membrane description of the black hole, appropriate to a distant observer. The technical analysis is illustrated in the simplified context of 1+1 dimensional dilaton gravity. Our postulates imply that the dissipative properties of the stretched horizon arise from a course graining of microphysical degrees of freedom that the horizon must possess. A principle of black hole complementarity is advocated. The overall viewpoint is similar to that pioneered by 't~Hooft but the detailed implementation is different.
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### Average Entropy of a Subsystem

(2010)
If a quantum system of Hilbert space dimension $$mn$$ is in a random pure state, the average entropy of a subsystem of dimension $$m\leq n$$ is conjectured to be $$S_{m,n}=\sum_{k=n+1}^{mn}\frac{1}{k}-\frac{m-1}{2n}$$ and is shown to be $$\simeq \ln m - \frac{m}{2n}$$ for $$1\ll m\leq n$$. Thus there is less than one-half unit of information, on average, in the smaller subsystem of a total system in a random pure state.
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### Author and article information

###### Journal
21 January 2013
2013-08-09
###### Article
10.1088/1475-7516/2013/09/028
1301.4995