  Due to the highly degeneracy and singularities of the entropy equation, the
physical entropy for viscous and heat conductive polytropic gases behave
singularly in the presence of vacuum and it is thus a challenge to study its
dynamics. It is shown in this paper that the uniform boundedness of the entropy
and the inhomogeneous Sobolev regularities of the velocity and temperature can
be propagated for viscous and heat conductive gases in $\mathbb R^3$, provided
that the initial vacuum occurs only at far fields with suitably slow decay of
the initial density. Precisely, it is proved that for any strong solution to
the Cauchy problem of the heat conductive compressible Navier--Stokes
equations, the corresponding entropy keeps uniformly bounded and the $L^2$
regularities of the velocity and temperature can be propagated, up to the
existing time of the solution, as long as the initial density vanishes only at
far fields with a rate no more than $O(\frac{1}{|x|^2})$. The main tools are
some singularly weighted energy estimates and an elaborate De Giorgi type
iteration technique. The De Giorgi type iterations are carried out to different
equations in establishing the lower and upper bounds of the entropy.
