An extension of the ideal hadron resonance gas (HRG) model is constructed which includes the attractive and repulsive van der Waals (VDW) interactions between baryons. This VDW-HRG model yields the nuclear liquid-gas transition at low temperatures and high baryon densities. The VDW parameters $a$ and $b$ are fixed by the ground state properties of nuclear matter, and the temperature dependence of various thermodynamic observables at zero chemical potential are calculated within the VDW-HRG model. Compared to the ideal HRG model, the inclusion of VDW interactions between baryons leads to a qualitatively different behavior of second and higher moments of fluctuations of conserved charges, in particular in the so-called crossover region $T\sim 140–190\mathrm{MeV}$. For many observables this behavior resembles closely the results obtained from lattice QCD simulations. This hadronic model also predicts nontrivial behavior of net-baryon fluctuations in the region of phase diagram probed by heavy-ion collision experiments. These results imply that VDW interactions play a crucial role in the thermodynamics of hadron gas. Thus, the commonly performed comparisons of the ideal HRG model with the lattice and heavy-ion data may lead to misconceptions and misleading conclusions.

The system-size dependence of hadrochemistry at vanishing baryon density is considered within the canonical statistical model (CSM) with local exact conservation of three conserved charges, allowing for a possibility of strangeness undersaturation, i.e., ${\gamma }_S\le 1$. Exact baryon number conservation is found to be even more important than that of strangeness in the canonical suppression picture at the CERN Large Hadron Collider, in contrast to intermediate and low collision energies. The model is applied to $p\text{−}p$, $p$-Pb, and Pb-Pb data of the ALICE Collaboration. A chemical equilibrium CSM with a fixed $T_{\mathrm{ch}}=155$ MeV describes the trends seen in most yield ratios. However, this “vanilla” version of CSM predicts an enhancement of the $\varphi /\pi$ ratio at smaller multiplicities, in stark contrast to the suppression seen in the data. The data are described with a 15% relative accuracy level whence a multiplicity dependence of both the temperature and the strangeness saturation parameter ${\gamma }_S\le 1$ is accepted. Both the canonical suppression and the strangeness undersaturation effects are small at $d{N}_{\mathrm{ch}}/d\eta \gtrsim 100$, but they do improve substantially the description of hadron yields in $p\text{−}p$ collisions, in particular the $\mathrm{\Omega }$ yields. A possibility to constrain the rapidity correlation volume using net-proton fluctuation measurements is pointed out.

The thermodynamic properties of high temperature and high density QCD matter are explored within the chiral SU(3)-flavor parity-doublet Polyakov-loop quark-hadron mean-field model, CMF. The quark sector of the CMF model is tuned to describe the ${\mu }_B=0$ thermodynamics data of lattice QCD. The resulting lines of constant physical variables as well as the baryon number susceptibilities are studied in some detail in the temperature–chemical-potential plane. The CMF model predicts three consecutive transitions: the nuclear first-order liquid-vapor phase transition, chiral symmetry restoration, and the crossover transition to a quark matter phase. All three phenomena are crossovers, for most of the $T\text{−}{\mu }_B$ plane. The deviations from the free ideal hadron gas baseline at ${\mu }_B=0$ and $T\approx 100\text{–}200$ MeV can be attributed to remnants of the liquid-vapor first-order phase transition in nuclear matter. The chiral crossing transition determines the baryon fluctuations at much higher ${\mu }_B\approx 1.5$ GeV. At high baryon densities, ${\mu }_B\approx 2.4$ GeV, the behavior of fluctuations is controlled by crossover to quark matter. The CMF model also describe well the static properties of high ${\mu }_B$ neutron stars as well as recent neutron star merger observations. The effective equation of state presented here describes simultaneously lattice QCD results at ${\mu }_B=0$ as well as observed physical phenomena (nuclear matter and neutron star matter) at $T\cong 0$ and high densities, ${\mu }_B>1$ GeV.

The first principle lattice QCD methods allow to calculate the thermodynamic observables at finite temperature and imaginary chemical potential. These can be compared to the predictions of various phenomenological models. We argue that Fourier coefficients with respect to imaginary baryochemical potential are sensitive to modeling of baryonic interactions. As a first application of this sensitivity, we consider the hadron resonance gas (HRG) model with repulsive baryonic interactions, which are modeled by means of the excluded volume correction. The Fourier coefficients of the imaginary part of the net-baryon density at imaginary baryochemical potential -- corresponding to the fugacity or virial expansion at real chemical potential -- are calculated within this model, and compared with the $N_t = 12$ lattice data. The lattice QCD behavior of the first four Fourier coefficients up to $T \simeq 185$ MeV is described fairly well by an interacting HRG with a single baryon-baryon eigenvolume interaction parameter $b \simeq 1$ fm$^3$, while the available lattice data on the difference $\chi_2^B - \chi_4^B$ of baryon number susceptibilities is reproduced up to $T \simeq 175$ MeV.Comment: 11 pages, 4 figures, new Fig. 2 depicting $\chi_2^B - \chi_4^B$, version accepted for publication in Physics Letters