  The homogeneous entropy for continuous systems in nonextensive statistics
reads $S^{H}_{q}=k_B\,{(1 - (K \int d\Gamma \rho^{1/q}(\Gamma))^{q})}/({1-q})$,
where $\Gamma$ is the phase space variable. Optimization of $S^{H}_{q}$
combined with normalization and energy constraints gives an implicit expression
of the distribution function $\rho (\Gamma)$ which can be computed explicitly
for the ideal gas. From this result, we compute properties such as the energy
fluctuations and the specific heat. Similar results are also presented using
the formulation based on the Tsallis entropy. From the analysis, we discuss the
validity of the application of the nonextensive formalism to continuous
Hamiltonian systems which is found to be restricted to the range $q<1$, which
renders problematic its applicability to the class of phenomena exhibiting
power law decay.
