序列效应代数中的rsamnyi熵和rsamnyi散度

IF 1.3 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Open Systems & Information Dynamics Pub Date : 2020-06-01 DOI:10.1142/s1230161220500080

Zahra Eslami Giski

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引用次数: 0

摘要

本研究的目的是将序列效应代数中关于Shannon熵和Kullback-Leibler散度的结果推广到r尼伊熵和r尼伊散度的情况。为此，提出了序列效应代数中有限分区的rsamnyi熵及其条件形式，并推导了这些熵测度的基本性质。在此基础上，引入了序列效应代数中分块的rsamunyi散度的概念，并研究了该量的基本性质。特别地，证明了给定序列效应代数中分区的Kullback-Leibler散度和Shannon熵可以分别作为它们的r nyi散度和r nyi熵的极限。最后，为了说明结果，给出了一些数值算例。

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Rényi Entropy and Rényi Divergence in Sequential Effect Algebra

The aim of this study is to extend the results concerning the Shannon entropy and Kullback–Leibler divergence in sequential effect algebra to the case of Rényi entropy and Rényi divergence. For this purpose, the Rényi entropy of finite partitions in sequential effect algebra and its conditional version are proposed and the basic properties of these entropy measures are derived. In addition, the notion of Rényi divergence of a partition in sequential effect algebra is introduced and the basic properties of this quantity are studied. In particular, it is proved that the Kullback–Leibler divergence and Shannon’s entropy of partitions in a given sequential effect algebra can be obtained as limits of their Rényi divergence and Rényi entropy respectively. Finally, to illustrate the results, some numerical examples are presented.

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来源期刊

Open Systems & Information Dynamics 工程技术-计算机：信息系统

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： The aim of the Journal is to promote interdisciplinary research in mathematics, physics, engineering and life sciences centered around the issues of broadly understood information processing, storage and transmission, in both quantum and classical settings. Our special interest lies in the information-theoretic approach to phenomena dealing with dynamics and thermodynamics, control, communication, filtering, memory and cooperative behaviour, etc., in open complex systems.