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

Year 2015, Volume: 12 Issue: 1, - , 01.05.2015

Zahra Eslami Giski Mohamad Ebrahimi

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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