  We derive the nonextensive thermodynamics of an ideal quantum gas composed by
bosons and/or fermions with finite chemical potentials. We find agreement with
previous works when $\mu \le m$, and some inconsistencies are corrected for
fermions when $\mu > m$. This formalism is then used to study the
thermodynamical properties of hadronic systems based on a Hadron Resonance Gas
approach. We apply this result to study the protoneutron star stability under
several conditions.
