Incomplete statistics: nonextensive generalizations of statistical mechanics

Statistical mechanics is generalized on the basis of incomplete information theory for inexact or incomplete probability distribution. An incomplete normalization ∑i=1w piq=1 with positive real q is proposed and, thanks to the q-deformed logarithmic function used as information measure leads to a nonextensive entropy: The resulting incomplete statistical mechanics is proved to have the same theoretical characteristics as the Tsallis one for complete probability distributions.