Entropy analysis of systems exhibiting negative probabilities

• Systems with negatives probabilities.
• Entropy generalization for negatives probabilities.
• Analogy between negatives probabilities and fractional derivatives.

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 Grünwald–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.