Thermodynamics of the PNJL model with nonzero baryon and isospin chemical potentials

We have extended the Polyakov-Nambu-Jona-Lasinio (PNJL) model for two degenerate flavours to include the isospin chemical potential ($\mu_I$). All the diagonal and mixed derivatives of pressure with respect to the quark number (proportional to baryon number) chemical potential ($\mu_0$) and isospin chemical potential upto sixth order have been extracted at $\mu_0 = \mu_I = 0$. These derivatives give the generalized susceptibilities with respect to quark and isospin numbers. Similar estimates for the flavour diagonal and off-diagonal susceptibilities are also presented. Comparison to Lattice QCD (LQCD) data of some of these susceptibilities for which LQCD data are available, show similar temperature dependence, though there are some quantitative deviations above the crossover temperature. We have also looked at the effects of instanton induced flavour-mixing coming from the $U_A(1)$ chiral symmetry breaking 't Hooft determinant like term in the NJL part of the model. The diagonal quark number and isospin susceptibilities are completely unaffected. The off-diagonal susceptibilities show significant dependence near the crossover. Finally we present the chemical potential dependence of specific heat and speed of sound within the limits of chemical potentials where neither diquarks nor pions can condense.