Entropy analysis of systems exhibiting negative probabilities

Abstract This paper addresses the concept of negative probability and its impact upon entropy. An analogy between the probability generating functions, in the scope of quasiprobability distributions, and the Grunwald–Letnikov definition of fractional derivatives, is explored. Two distinct cases producing negative probabilities are formulated and their distinct meaning clarified. Numerical calculations using the Shannon entropy characterize further the characteristics of the two limit cases.

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