Thermodynamics and susceptibilities of isospin imbalanced QCD matter

We study the thermodynamics and the susceptibilities of quark matter in the framework of two-flavor Nambu-Jona-Lasinio model at finite isospin chemical potential and temperature. Isospin number density, normalized energy density and trace anomaly are shown to be in good agreement with the available lattice data as well as with the results from chiral perturbation theory at zero temperature. We also study how susceptibilities depend on the isospin chemical potential and on temperature. We find a peak for the chiral, pion, and isospin susceptibilities at the critical isospin chemical potential, $\mu_I^c(T)$, at the boundary of the phase transition between the normal and pion superfluid phase. Moreover, temperature makes the transition from normal to pion condended phase smoother. We also note that the pion susceptibility always remains zero in the normal phase while it is finite in the superfluid phase.