  We have applied the non-extensive statistical mechanics to free electrons in
several metals to calculate the electronic specific heat at low temperature. In
this case, the Fermi-Dirac (FD) function is modified from its Boltzmann-Gibbs
(BG) form, with the exponential part going to a $q$-exponential, in its
non-extensive form. In most cases, the non-extensive parameter, $q$, is found
to be greater than unity to produce the correct thermal effective mass, $m^*$,
of electrons. The ratio $m^*/m$ is found to show a nice systematic dependence
on $q$. Results indicate, electrons in metals, in the presence of long range
correlations are reasonably well described by Tsallis statistics.
