  The generalized non-extensive statistics proposed by Tsallis have been
successfully utilized in many systems where long range interactions are
present. For high density quark matter an attractive long range interaction
arising from single gluon exchange suggests the formation of a diquark
condensate. We study the effects on this color superconducting phase for two
quark flavors due to a change to Tsallis statistics. By numerically solving the
gap equation we obtain a generalization of the universality condition,
$\frac{2\phi_{0}}{T_{C}}\approx 3.52$ and determine the temperature dependence
of the gap. For the Tsallis parameter $q\approx 1$ the specific heat is
exponential becoming more linear as q increases. This suggests that for larger
values of q s-wave color superconductors behave like high $T_c$ superconductors
rather than weak superconductors.
