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Finite-Temperature Quarkyonic Matter with an Excluded Volume Model

We introduce a theoretical framework to analyze the thermal properties of a recently proposed "excluded volume" model of quarkyonic matter. This entails proposing finite temperature distribution functions and entropy functionals constrained by internal theoretical consistency. We use the formalism developed here to analyze the effect of temperature on the quark onset as a function of baryon density. We find that the baryon density at which the quarkyonic phase emerges decreases only slightly with temperature, an effect produced by large $N_c$. We furthermore find that a finite temperature increases the density of quarks produced. The framework presented here can be used to compute the equation of state of hot and dense quarkyonic matter which is of relevance to neutron star mergers.