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.

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• Equations of state of nuclear matter
• QCD phase transitions
• QCD phenomenology
• Relativistic heavy-ion collisions