Black hole entropy is proposed to equal the Kullback-Leibler divergence between a mass-biased N-bit ensemble and the uniform ensemble, with the area law as the leading 1/N term.
Geometry of black hole thermodynamics
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The Hessian of the entropy function can be thought of as a metric tensor on the state space. In the context of thermodynamical fluctuation theory Ruppeiner has argued that the Riemannian geometry of this metric gives insight into the underlying statistical mechanical system; the claim is supported by numerous examples. We study this geometry for some families of black holes. It is flat for the BTZ and Reissner-Nordstrom black holes, while curvature singularities occur for the Reissner-Nordstrom-anti-de Sitter and Kerr black holes.
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Information-Theoretic Black Hole Entropy I: Beyond the Area Law
Black hole entropy is proposed to equal the Kullback-Leibler divergence between a mass-biased N-bit ensemble and the uniform ensemble, with the area law as the leading 1/N term.