Machado, J. A. Tenreiro2017-01-252015http://hdl.handle.net/10400.22/9401This paper addresses the concept of negative probability and its impact upon entropy. An anal-ogy between the probability generating functions, in the scope of quasiprobability distribu-tions, and the Grünwald–Letnikov definition of fractional derivatives, is explored. Two distinct cases producing negative probabilities are formulated and their distinct meaning clarified. Nu-merical calculations using the Shannon entropy characterize further the characteristics of the two limit cases.engEntropyNegative probabilityFractional calculusQuasiprobability distributionsjournal articlehttp://dx.doi.org/10.1016/j.cnsns.2015.11.022