  In this work we use the extremization method of various information-theoretic
measures (Fisher information, Shannon entropy, Tsallis entropy) for
$d$-dimensional quantum systems, which complementary describe the spreading of
the quantum states of natural systems. Under some given constraints, usually
one or two radial expectation values, this variational method allows us to
determine an extremum-entropy distribution, which is the \textit{least-biased}
one to characterize the state among all those compatible with the known data.
Then we use it, together with the spin-dependent uncertainty-like relations of
Daubechies-Thakkar type, as a tool to obtain relationships between the position
and momentum radial expectation values of the type $\langle
r^{\alpha}\rangle^{\frac{k}{\alpha}}\langle p^k\rangle\geq f(k,\alpha,q,N),
q=2s+1$, for $d$-dimensional systems of $N$ fermions with spin $s$. The
resulting uncertainty-like products, which take into account both spatial and
spin degrees of freedom of the fermionic constituents of the system, are shown
to often improve the best corresponding relationships existing in the
literature.
