  Gibbs-Boltzmann entropy leads to systems that have a strong dependence on
initial conditions. In reality, most materials behave quite independently of
initial conditions. Nonextensive entropy or Tsallis entropy leads to
nonextensive statistical mechanics. In this paper, we calculate the Tsallis
form of Clausius inequality and then determine the upper bound for extracting
work from the small system in the nonextensive statistical mechanics with
mutual information. In the following, we extract mutual information and adjust
Maxwell's demon with quantum feedback control.
