Merging multidimensional equations of state of strongly interacting matter via a statistical mixture

TL;DR

This paper presents a novel method to merge multiple equations of state into a single, thermodynamically consistent EoS that can handle phase transitions and critical points, useful for heavy-ion collision simulations.

Contribution

A general statistical mixture approach to combine multidimensional EoSs into a unified, stable, and thermodynamically consistent EoS capable of modeling complex phase structures.

Findings

Successfully merged hadronic and deconfined matter EoSs.

Maintained thermodynamic stability and consistency in the merged EoS.

Demonstrated applicability in heavy-ion collision simulations.

Abstract

We introduce a general method to merge multidimensional equations of state (EoSs) by combining them in a two-fluid equilibrium statistical mixture in the grand canonical ensemble. The merged grand potential density $\omega$ is built directly from the input EoSs and the fluid fractions are fixed by minimizing $\omega$ at fixed temperature $T$ and baryon chemical potential $\mu_B$. Thermodynamic consistency and stability are guaranteed as all thermodynamic quantities are consistently derived from a single merged grand potential $\omega(T,\mu_B)$ with the correct convexity properties. Our method can accommodate a first-order phase transition and a critical endpoint with mean-field critical exponents. We use this method to merge a van der Waals Hadron-Resonance-Gas EoS with a holographic Einstein-Maxwell-Dilaton EoS that has a critical point and a first-order line. The result is a single EoS, spanning hadronic and deconfined matter over a broad range in $(T,\mu_B)$, which can be readily used in heavy-ion hydrodynamic simulations. Our merging method can be generalized to consider a higher dimensional phase diagram (e.g., by considering more chemical potentials) and more than two input EoSs.