Generalized bit- moments and cumulants based on discrete derivative
arXiv:cond-mat/0110310 · doi:10.1016/S0375-9601(02)00142-1
Abstract
We give a simple recipe based on the use of discrete derivative, to obtain generalized bit-moments obeying nonadditive statistics of Tsallis. The generalized bit-cumulants may be of two kinds, first which preserve the standard relations between moments and cumulants of a distribution, and are nonadditive with respect to independent subsystems. The second kind do not preserve usual moment-cumulant relations. These are additive in nature and Renyi entropy is naturally incorporated as the cumulant of order one.
Latex 10 pages