  It is believed that quark matter can exist in neutron star interior if the
baryon density is high enough. When there is a large isospin density, quark
matter could be in a pion condensed phase. We compute neutrino emission from
direct Urca processes in such a phase, particularly in the inhomogeneous
Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) states. The neutrino emissivity and
specific heat are obtained, from which the cooling rate is estimated.
