  The non-monotonic behavior of the speed of sound for isospin imbalanced
strongly interacting matter, found by recent lattice QCD simulations, can be
reproduced within the Nambu--Jona-Lasinio model and Linear Sigma Model with
quarks when the couplings become isospin chemical potential-dependent. The
introduction of medium-dependent couplings can potentially affect the
equivalence between the thermodynamic relations and their definitions from
statistical mechanics. We describe the procedure to compensate for the
introduction of medium-dependent couplings to preserve the correct
thermodynamic identities. We find the isospin chemical potential dependence for
the couplings from the isospin density LQCD data and, after finding the
compensating function to correctly describe the pressure, we show that the
description of the square of the speed of sound reported by LQCD is well
reproduced when using the found medium-dependent couplings in both models.
