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Isentropic thermodynamics across the hadron-quark mixed phase in a two-phase model with a PNJL quark description

Eduardo L. G. Salgado*, Pedro Costa†, and Constança Providência‡

  • *Contact author: uc2020216840@student.uc.pt
  • †Contact author: pcosta@uc.pt
  • ‡Contact author: cp@fis.uc.pt
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Phys. Rev. D 114, 014042 – Published 20 July, 2026

DOI: https://doi.org/10.1103/ltq6-ryt9

Abstract

We study the hadron-quark mixed phase within a two-phase model for symmetric and asymmetric matter. For the quark sector we employ the (2+1) Polyakov-extended Nambu–Jona-Lasinio model (PNJL) with vector interactions. We investigate how the hadronic equation of state affects the phase diagram and the thermodynamic properties inside the mixed phase. The behavior of isentropic trajectories in the mixed phase depends on the fixed entropy per baryon (s/ρB), with trajectories near the critical end point (CEP) exhibiting a pronounced cooling pattern, while isentropic trajectories with low entropy per baryon undergo pronounced heating as the baryonic density increases. The adiabatic squared speed of sound displays characteristic peak and dip structures that depend on s/ρB. The polytropic index along isentropic and isothermal trajectories, including in the vicinity of the CEP are also investigated. The effects of vector interactions and isospin asymmetry on thermodynamic observables likewise depend on the chosen s/ρB value. Finally, we discuss the population of hyperons along isentropic trajectories and their influence on the phase diagram. The main effect of hyperons is to shift the onset of deconfinement to larger densities and decrease the density extension of the mixed phase.

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Phys. Rev. D 114, 014042– Published 20 July, 2026
  • Received 16 March 2026
  • Accepted 25 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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