Entropy of Countable Partitions on Effect Algebra with Rieze Decomposition Property and Weak Sequential Effect Algebra

Authors : Zahra Eslami Giski, Mohamad Ebrahimi

Pages : 0-0

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Publication Date : 2015-05-01

Article Type : Research Paper

Abstract :The purpose of this study is twofold. For the first part, the entropy of countable partitions on an effect algebra with the Riesz decomposition property is defined. In addition, the lower and upper entropy and the conditional entropy considering a suitable state and transformation functions are introduced. Then, some basic properties of these notions are investigated. In the second part, weak sequential effect algebra is introduced followed by a definition for the entropy of countable partitions on this structure. Furthermore, with the help of appropriate state and transformation functions, the notion of entropy, conditional entropy and relative entropy are introduced. In the final step, some properties of these concepts are studied.
Keywords : Entropy, Effect algebra, Dynamical system, Sequential effect algebra

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