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Keywords:
effect algebra; Riesz decomposition property; MV-algebra; state; entropy
effect algebra; Riesz decomposition property; MV-algebra; state; entropy
Summary:
We define the entropy, lower and upper entropy, and the conditional entropy of a dynamical 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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