Entropy on effect algebras with the Riesz decomposition property I: Basic properties

Abstract

We define the entropy, lower and upper entropy, and the conditional entropy of a dy­ namical system consisting of an effect algebra with the Riesz decomposition property, a state, and a transformation. Such effect algebras allow many refinements of two partitions. We present the basic properties of these entropies and these notions are illustrated by many examples. Entropy on MV-algebras is postponed to Part II.

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@article{Nola2005EntropyOE, title={Entropy on effect algebras with the Riesz decomposition property I: Basic properties}, author={Antonio di Nola and Anatolij Dvurecenskij and Marek Hycko and Corrado Manara}, journal={Kybernetika}, year={2005}, volume={41}, pages={143-160} }