  The influence of correlations of uniform Fermi systems (nuclear matter,
electron gas and liquid $^3$He) on Shannon's information entropy, $S$, is
studied. $S$ is the sum of the information entropies in position and momentum
spaces. It is found that, for three different Fermi systems with different
particle interactions, the correlated part of $S$ ($S_{cor}$) depends on the
correlation parameter of the systems or on the discontinuity gap of the
momentum distribution through two parameter expressions. The values of the
parameters characterize the strength of the correlations. A two parameter
expression also holds between $S_{cor}$ and the mean kinetic energy ($K$) of
the Fermi system. The study of thermal effects on the uncorrelated electron gas
leads to a relation between the thermal part of $S$ ($S_{thermal}$) and the
fundamental quantities of temperature, thermodynamical entropy and the mean
kinetic energy. It is found that, in the case of low temperature limit, the
expression connecting $S_{thermal}$ with $K$ is the same to the one which
connects $S_{cor}$ with $K$. There are only some small differences on the
values of the parameters. Thus, regardless of the reason (correlations or
thermal) that changes $K$, $S$ takes almost the same value.
