The previous thermodynamic treatment for models with density and/or temperature dependent quark masses is shown to be inconsistent with the requirement of fundamental thermodynamics. We therefore study a fully self-consistent one according to the fundamental differential equation of thermodynamics. After obtaining a new quark mass scaling with the inclusion of both confinement and leading-order perturbative interactions, we investigate properties of strange quark matter in the fully consistent thermodynamic treatment. It is found that the equation of state become stiffer, and accordingly, the maximum mass of strange stars is as large as about 2 times the solar mass, if strange quark matter is absolutely or metastable.

At low energies, the strong interaction is governed by the Goldstone bosons associated with the spontaneous chiral symmetry breaking, which can be systematically described by chiral perturbation theory. In this paper, we apply this theory to study the θ-vacuum energy density and hence the QCD axion potential up to next-to-leading order with N non-degenerate quark masses. By setting N = 3, we then derive the axion mass, self-coupling, topological susceptibility and the normalized fourth cumulant both analytically and numerically, taking the strong isospin breaking effects into account. In addition, the model-independent part of the axion-photon coupling, which is important for axion search experiments, is also extracted from the chiral Lagrangian supplemented with the anomalous terms up to $$ \mathcal{O}\left({p}^6\right) $$O p 6 .

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, $$\mu _I^c(T)$$μIc(T) , at the boundary of the phase transition between the normal and pion superfluid phase. Moreover, temperature makes the transition from normal to pion condensed phase smoother. We also note that the pion susceptibility always remains zero in the normal phase while it is finite in the superfluid phase.

We study the influence of external parallel electric and magnetic fields and a chiral chemical potential ${\mu }_5$ on the chiral phase transition of quantum chromodynamics. Our theoretical framework is a Nambu–Jona-Lasinio model with a contact interaction. Within this model we compute the critical temperature of chiral symmetry restoration $T_c$ as a function of the chiral chemical potential and field strengths. We find that the fields inhibit and ${\mu }_5$ enhances chiral symmetry breaking, in agreement with previous studies.

We compute the effect of the chiral phase transition of QCD on the axion mass and self-coupling; the coupling of the axion to the quarks at finite temperature is described within the Nambu–Jona-Lasinio model. We find that the axion mass decreases with temperature, following the response of the topological susceptibility, in agreement with previous results obtained within chiral perturbation theory at low and intermediate temperatures. As expected, the comparison with lattice data shows that chiral perturbation theory fails to reproduce the topological susceptibility around the chiral critical temperature, while the Nambu–Jona-Lasinio model offers a better qualitative agreement with these data, hence a more reliable estimate of the temperature dependence of the axion mass in the presence of a hot quark medium. We complete our study by computing the temperature dependence of the self-coupling of the axion, finding that this coupling decreases at and above the phase transition. The model used in our work as well as the results presented here pave the way to the computation of the in-medium effects of hot and/or dense quark-gluon plasma on the axion properties.