# A Phenomenological Equation of State of Strongly Interacting Matter with First-Order Phase Transitions and Critical Points

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Model

#### 2.1. Relativistic Energy Density Functional with Modified Excluded-Volume Mechanism

#### 2.2. Available-Volume Fractions and Model Parameters

^{−3}), binding energy at saturation ($B=16.02$ MeV), incompressibility ($K=242.7$ MeV), symmetry energy ($J=32.73$ MeV), and slope ($L=57.94$ MeV), that are consistent with modern constraints from experiment and theory.

^{3}, ${T}_{0}=270$ MeV, and ${n}_{\mathrm{cut}}={n}_{\mathrm{sat}}$ of the DD2 parametrization.

## 3. Results

^{−3}, well above the nuclear saturation density ${n}_{\mathrm{sat}}$. At higher temperatures, it moves to lower densities with an almost constant extension in baryon density except for temperatures close to ${T}_{\mathrm{crit}}$. Here, the critical density is found as 0.201 fm

^{−3}, still above ${n}_{\mathrm{sat}}$. The dashed line in panel (a) marks the boundary between regions without (lower left) and with (upper right) effects of the modified EV mechanism in the present parametrization. It corresponds to the condition $x=0$. There is another region in the phase diagram without modified EV effects at temperatures above ${T}_{0}$, outside the figure.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

CCSN | core-collapse supernova |

EoS | equation of state |

EV | excluded-volume |

HIC | heavy-ion collision |

NS | neutron star |

PT | phase transition |

QCD | quantum chromodynamics |

RMF | relativistic mean-field |

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**Figure 1.**Isotherms in isospin-symmetric strongly interacting matter in the pressure–baryon density diagram at temperatures from 0 to 160 MeV in steps of 20 MeV (dashed colored lines) and at the critical temperature ${T}_{\mathrm{crit}}$ of the pseudo hadron–quark phase transition (black dot-dashed line). The binodals and critical points are denoted by full black lines and a full (open) circle of the pseudo hadron–quark (liquid-gas) phase transition, respectively.

**Figure 2.**Binodals (full lines) and critical points (full and open circles) of isospin-symmetric strongly interacting matter in (

**a**) the temperature–baryon density diagram and (

**b**) the temperature–baryon chemical potential diagram. The dashed line in panel (

**a**) separates the region without effects of the modified excluded-volume mechanism (lower left) from the region with effects (upper right). Results for the liquid–gas phase transition are shown at subsaturation densities.

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Typel, S.; Blaschke, D. A Phenomenological Equation of State of Strongly Interacting Matter with First-Order Phase Transitions and Critical Points. *Universe* **2018**, *4*, 32.
https://doi.org/10.3390/universe4020032

**AMA Style**

Typel S, Blaschke D. A Phenomenological Equation of State of Strongly Interacting Matter with First-Order Phase Transitions and Critical Points. *Universe*. 2018; 4(2):32.
https://doi.org/10.3390/universe4020032

**Chicago/Turabian Style**

Typel, Stefan, and David Blaschke. 2018. "A Phenomenological Equation of State of Strongly Interacting Matter with First-Order Phase Transitions and Critical Points" *Universe* 4, no. 2: 32.
https://doi.org/10.3390/universe4020032