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We investigate extensions of the Hadron Resonance Gas (HRG) Model beyond the ideal case by incorporating both attractive and repulsive interactions into the model. When considering additional states exceeding those measured with high confidence by the Particle Data Group, attractive corrections to the overall pressure in the HRG model are imposed. On the other hand, we also apply excluded-volume corrections, which ensure there is no overlap of baryons by turning on repulsive (anti)baryon-(anti)baryon interactions. We emphasize the complementary nature of these two extensions and identify combinations of conserved charge susceptibilities that allow us to constrain them separately. In particular, we find interesting ratios of susceptibilities that are sensitive to one correction and not the other. This allows us to constrain the excluded volume and particle spectrum effects separately. Analysis of the available lattice results suggests the presence of both the extra states in the baryonstrangeness sector and the repulsive baryonic interaction, with indications that hyperons have a smaller repulsive core than non-strange baryons. We note that these results are interesting for heavy-ion-collision systems at both the LHC and RHIC. 

By using gravity/gauge correspondence, we construct a holographic model, constrained to mimic the lattice QCD equation of state at zero density, to investigate the temperature and baryon chemical potential dependence of the equation of state. We also obtained the energy loss of light and heavy partons within the hot and dense plasma represented by the heavy quark drag force, Langevin diffusion coefficients and jet quenching parameter at the critical point and across the first-order transition line predicted by the model. 

By using gravity/gauge correspondence, we employ an Einstein-Maxwell-Dilaton model to compute the equilibrium and out-of-equilibrium properties of a hot and baryon rich strongly coupled quark-gluon plasma. The family of 5-dimensional holographic black holes, which are constrained to mimic the lattice QCD equation of state at zero density, is used to investigate the temperature and baryon chemical potential dependence of the equation of state. We also obtained the baryon charge conductivity, and the bulk and shear viscosities with a particular focus on the behavior of these observables on top of the critical end point and the line of first order phase transition predicted by the model. 

In this contribution we present a resummation of the Quantum Chromodynamics (QCD) equation of state from lattice simulations at imaginary chemical potentials. We generalize the scheme introduced in a previous work [1], to the case of non-zero strangeness chemical potential. We present continuum extrapolated results for thermodynamic observables in the temperature range 130MeV ≤ T ≤ 280 MeV, for chemical potentials up to μ B / T = 3:5, along the strangeness neutral line. Furthermore, we relax the constraint of strangeness neutrality, by extrapolating to small values of the strangeness-to-baryon-number ratio R = n S / n B . 

The equation of state (EoS) of QCD is a crucial input for the modeling of heavy-ion-collision (HIC) and neutron-star-merger systems. Calculations of the fundamental theory of QCD, which could yield the true EoS, are hindered by the infamous Fermi sign problem which only allows direct simulations at zero or imaginary baryonic chemical potential. As a direct consequence, the current coverage of the QCD phase diagram by lattice simulations is limited. In these proceedings, two different equations of state based on first-principle lattice QCD (LQCD) calculations are discussed. The first is solely informed by the fundamental theory by utilizing all available diagonal and non-diagonal susceptibilities up to O(µ 4 B) in order to reconstruct a full EoS at finite baryon number, electric charge and strangeness chemical potentials. For the second, we go beyond information from the lattice in order to explore the conjectured phase structure, not yet determined by LQCD methods, to assist the experimental HIC community in their search for the critical point. We incorporate critical behavior into this EoS by relying on the principle of universality classes, of which QCD belongs to the 3D Ising Model. This allows one to study the effects of a singularity on the thermodynamical quantities that make up the equation of state used for hydrodynamical simulations of HICs. Additionally, we ensure that these EoSs are valid for applications to HICs by enforcing conditions of strangeness neutrality and fixed charge-to-baryonnumber ratio.