  Gibbs' theorem, which is originally intended for canonical ensembles with
complete statistics has been generalized to open systems with incomplete
statistics. As a result of this generalization, it is shown that the stationary
equilibrium distribution of inverse power law form associated with the
incomplete statistics has maximum entropy even for open systems with energy or
matter influx. The renormalized entropy definition given in this paper can also
serve as a measure of self-organization in open systems described by incomplete
statistics.
