  Shannon entropy in position ($S_{\rvec}$) and momentum ($S_{\pvec}$) spaces,
along with their sum ($S_t$) are presented for unit-normalized densities of He,
Li$^+$ and Be$^{2+}$ ions, spatially confined at the center of an impenetrable
spherical enclosure defined by a radius $r_c$. Both ground as well as some
selected low-lying singly excited states, \emph{viz.,} 1sns (n $=$ 2-4) $^3$S,
1snp (n $=$ 2-3) $^3$P, 1s3d $^3$D are considered within a density functional
methodology that makes use of a work-function-based exchange potential along
with two correlation potentials (local Wigner-type parametrized functional as
well as the more involved non-linear gradient- and Laplacian-dependent
Lee-Yang-Parr functional). The radial Kohn-Sham (KS) equation is solved using
an optimal spatial discretization scheme via the generalized pseudospectral
(GPS) method. A detailed systematic analysis of the confined system (relative
to corresponding free system) has been performed for these quantities with
respect to $r_c$ in tabular and graphical forms, \emph{with and without}
electron correlation. Due to compression, the pattern of entropy in
aforementioned states gets characterized by various crossovers at intermediate
and lower $r_c$ regions. The impact of electron correlation is more pronounced
in weaker confinement limit, and appears to decay with rise in confinement
strength. The exchange-only results are quite good to provide a decent
qualitative discussion. The lower-bounds provided by entropic uncertainty
relation holds good in all cases. Several other new interesting features are
observed.
