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.

The symmetry energy obtained with the effective Skyrme energy density functional is related to the values of isoscalar effective mass and isovector effective mass, which is also indirectly related to the incompressibility of symmetric nuclear matter. In this work, we analyze the values of symmetry energy and its related nuclear matter parameters in five-dimensional parameter space by describing the heavy ion collision data, such as isospin diffusion data at 35 MeV/u and 50 MeV/u, neutron skin of ${}^{208}\mathrm{Pb}$, and tidal deformability and maximum mass of neutron star. We obtain the parameter sets which can describe the isospin diffusion, neutron skin, tidal deformability, and maximum mass of neutron star, and give the incompressibility $K_0=250.23\pm 20.16$ MeV, symmetry energy coefficient $S_0=31.35\pm 2.08$ MeV, the slope of symmetry energy $L=59.57\pm 10.06$ MeV, isoscalar effective mass $m_s^{*}/m=0.75\pm 0.05$, and quantity related to effective mass splitting $f_I=0.005\pm 0.170$. At two times normal density, the symmetry energy we obtained is in 35–55 MeV. To reduce the large uncertainties of $f_I$, more critical works in heavy ion collisions at different beam energies are needed.

In the framework of the Thomas-Fermi approximation, we systematically study the EOSs and microscopic structures of neutron star matter in a vast density range with n _b ≈ 10⁻¹⁰-2 fm⁻³, where various covariant density functionals are adopted, i.e., those with nonlinear self couplings (NL3, PK1, TM1, GM1, MTVTC) and density-dependent couplings (DD-LZ1, DDME-X, PKDD, DD-ME2, DD2, TW99). It is found that the EOSs generally coincide with each other at n _b ≲ 10⁻⁴ fm⁻³ and 0.1 fm⁻³ ≲ n _b ≲ 0.3 fm⁻³, while in other density regions they are sensitive to the effective interactions between nucleons. By adopting functionals with a larger slope of symmetry energy L, the curvature parameter K _sym and neutron drip density generally increases, while the droplet size, proton number of nucleus, core-crust transition density, and onset density of non-spherical nuclei, decrease. All functionals predict neutron stars with maximum masses exceeding the two-solar-mass limit, while those of DD2, DD-LZ1, DD-ME2, and DDME-X predict optimum neutron star radii according to the observational constraints. Nevertheless, the corresponding skewness coefficients J are much larger than expected, while only the functionals MTVTC and TW99 meet the start-of-art constraints on J. More accurate measurements on the radius of PSR J0740 + 6620 and the maximum mass of neutron stars are thus essential to identify the functional that satisfies all constraints from nuclear physics and astrophysical observations. Approximate linear correlations between neutron stars’ radii at M = 1.4M _⊙ and 2M _⊙, the slope L and curvature parameter K _sym of symmetry energy are observed as well, which are mainly attributed to the curvature-slope correlations in the functionals adopted here. The results presented here are applicable for investigations of the structures and evolutions of compact stars in a unified manner.

We explore the effects of strangeness and $\mathrm{\Delta }$ resonance in baryonic matter and compact stars within the relativistic-mean-field models. The parameter set PKDD is adopted for $N\text{−}N$ interaction, parameters fixed based on finite hypernuclei and neutron stars are taken for the hyperon-meson couplings, and the universal baryon-meson coupling scheme is adopted for the $\mathrm{\Delta }$-meson couplings. In light of the recent observations of GW170817 with the dimensionless combined tidal deformability $197\le \overline{\mathrm{\Lambda }}\le 720$, we find it is essential to include the $\mathrm{\Delta }$ resonances in compact stars, and small $\mathrm{\Delta }\text{−}\rho$ coupling $g_{\rho \mathrm{\Delta }}$ is favored if the mass ${2.27}_{-0.15}^{+0.17}{M}_{\odot }$ of PSR $\mathrm{J}2215+5135$ is confirmed.

We study the interface effects of a quark-hadron mixed phase in compact stars. The properties of nuclear matter are obtained based on the relativistic-mean-field model. For the quark phase, we adopt a perturbation model with running quark masses and coupling constant. At certain choices of parameter sets, it is found that varying the quark-hadron interface tension will have sizable effects on the radii ($\mathrm{\Delta }R\approx 600\mathrm{m}$) and tidal deformabilities ($\mathrm{\Delta }\mathrm{\Lambda }/\mathrm{\Lambda }\approx 50\%$) of 1.36 solar mass hybrid stars. These provide possibilities for us to constrain the quark-hadron interface tension with future gravitational wave observations as well as the ongoing NICER mission.