Journal of Theoretical and Computational Studies
GENERAL EXTENSIVE GRAND CANONICAL PARTITION FUNCTION
Research Group on Theoretical and Mathematical Physics, Department of Physics, Gadjah Mada University, Bulaksumur Yogyakarta 55281, Indonesia.
By requiring the extensivity of the grand canonical partition function for a system of identical particles obeying permutation invariant, we obtained a ``strong cluster decomposition condition''. Coupled with the requirement to have a unitarity theory, the condition leads to a classification of all extensive and unitary quantum statistical systems. Besides encompassing the known Bose and Fermi statistics, the classification also consist of an infinitely many new statistics that we call fuzzy statistics.