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The non-monotonic behavior of the speed of sound for isospin imbalancedstrongly interacting matter, found by recent lattice QCD simulations, can bereproduced within the Nambu--Jona-Lasinio model and Linear Sigma Model withquarks when the couplings become isospin chemical potential-dependent. Theintroduction of medium-dependent couplings can potentially affect theequivalence between the thermodynamic relations and their definitions fromstatistical mechanics. We describe the procedure to compensate for theintroduction of medium-dependent couplings to preserve the correctthermodynamic identities. We find the isospin chemical potential dependence forthe couplings from the isospin density LQCD data and, after finding thecompensating function to correctly describe the pressure, we show that thedescription of the square of the speed of sound reported by LQCD is wellreproduced when using the found medium-dependent couplings in both models.

Describing the speed of sound peak of isospin-asymmetric cold strongly interacting matter using effective models