Rényi entropy
Concept in information theory / From Wikipedia, the free encyclopedia
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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. The Rényi entropy is named after Alfréd Rényi, who looked for the most general way to quantify information while preserving additivity for independent events.[1][2] In the context of fractal dimension estimation, the Rényi entropy forms the basis of the concept of generalized dimensions.[3]
The Rényi entropy is important in ecology and statistics as index of diversity. The Rényi entropy is also important in quantum information, where it can be used as a measure of entanglement. 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.[4][5] In theoretical computer science, the min-entropy is used in the context of randomness extractors.