9/3/2023 0 Comments Entanglement entropyKnowledge of the actual probabilities allows a player to profit from the game. Financial interpretation Ī pair of probability distributions can be viewed as a game of chance in which one of the distributions defines official odds and the other contains the actual probabilities. 1 Introduction An interesting attempt to understand the Bekenstein-Hawking formula of black hole entropy SBH A /4 G, with A the black hole horizon area and G the gravitational constant, is to relate it to the entanglement entropy ( SE) across the black hole horizon 1 5. For any fixed distributions P and Q, the Rényi divergence is nondecreasing as a function of its order α, and it is continuous on the set of α for which it is finite, or for the sake of brevity, the information of order α obtained if the distribution P is replaced by the distribution Q. The Rényi entropy of order α is greater than or equal to zero, and zero only when P = Q. In theoretical computer science, the min-entropy is used in the context of randomness extractors. In the Heisenberg XY spin chain model, the Rényi entropy as a function of α can be calculated explicitly because it is an automorphic function with respect to a particular subgroup of the modular group. The Rényi entropy is also important in quantum information, where it can be used as a measure of entanglement. The Rényi entropy is important in ecology and statistics as index of diversity. In the context of fractal dimension estimation, the Rényi entropy forms the basis of the concept of generalized dimensions. The Rényi entropy is named after Alfréd Rényi, who looked for the most general way to quantify information while preserving additivity for independent events. In information theory, the Rényi entropy is a quantity that generalizes various notions of entropy, including Hartley entropy, Shannon entropy, collision entropy, and min-entropy.
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