© 2015, The Author(s). In the present work we apply non-extensive statistics to obtain equations of state suitable to describe stellar matter and verify its effects on microscopic and macroscopic quantities. Two snapshots of the star evolution are considered and the direct Urca process is investigated with two different parameter sets. q-values are chosen as 1.05 and 1.14. The equations of state are only slightly modified, but the effects are enough to produce stars with slightly higher maximum masses. The onsets of the constituents are more strongly affected and the internal stellar temperature decreases with the increase of the q-value, with consequences on the strangeness and cooling rates of the stars.