Framework for phase transitions between the Maxwell and Gibbs constructions at finite temperature

Constantinos Constantinou; Mirco Guerrini; Tianqi Zhao; Sophia Han; Madappa Prakash

doi:10.1103/8l3m-tdlc

Framework for phase transitions between the Maxwell and Gibbs constructions at finite temperature

Constantinos Constantinou ^1,2,*, Mirco Guerrini ^3,4,†, Tianqi Zhao ^5,6,7,‡, Sophia Han ^8,9,7,10,§, and Madappa Prakash ^5,∥

¹INFN-TIFPA, Trento Institute of Fundamental Physics and Applications, Povo, 38123 Trento, Italy
²European Centre for Theoretical Studies in Nuclear Physics and Related Areas, Villazzano, 38123 Trento, Italy
³Department of Physics and Earth Science, University of Ferrara, 44122 Ferrara, Italy
⁴INFN, Sezione di Ferrara, 44122 Ferrara, Italy
⁵Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701, USA
⁶Institute for Nuclear Theory, University of Washington, Seattle, Washington 98195, USA
⁷Network for Neutrinos, Nuclear Astrophysics, and Symmetries (N3AS), University of California, Berkeley, Berkeley, California 94720, USA
⁸Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 201210, China
⁹School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
¹⁰State Key Laboratory of Dark Matter Physics, Shanghai Jiao Tong University, Shanghai 201210, China

^*Contact author: cconstantinou@ectstar.eu
^†Contact author: mirco.guerrini@unife.it
^‡Contact author: tianqi.zhao@berkeley.edu
^§Contact author: sjhan@sjtu.edu.cn
^∥Contact author: prakash@ohio.edu

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Phys. Rev. D 112, 094014 – Published 10 November, 2025

DOI: https://doi.org/10.1103/8l3m-tdlc

Abstract

The characteristics of the hadron-to-quark first-order phase transition differ depending on whether charge neutrality is locally or globally fulfilled. In $β$ -equilibrated matter, these two possibilities correspond to the Maxwell and Gibbs constructions. Recently, we presented a new framework in which a continuously varying parameter allows one to describe a first-order phase transition in intermediate scenarios to the two extremes of fully local and fully global charge neutrality. In this work, we extend the previous framework to finite temperatures and out-of- $β$ equilibrium conditions, making it available for simulations of core-collapse supernovae and binary neutron star mergers. We investigate its impact on key thermodynamic quantities across a range of baryon densities, temperatures, and electron fractions. We find that when matter is not in $β$ equilibrium, the pressure in the mixed phase is not constant even for the case of fully local charge neutrality. Moreover, we compute the thermal index using three different approaches, demonstrating that the finite-temperature extension of an equation of state using a constant thermal index can be ill defined when applied to the mixed phase.

Physical Review D

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Framework for phase transitions between the Maxwell and Gibbs constructions at finite temperature

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Framework for phase transitions between the Maxwell and Gibbs constructions at finite temperature

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