3 -60 -40 -20 0 -60 -40 -20 0 $_{µ}$p,n  (MeV) 0 0.2 0.4 0.6 0.8 -60 -40 -20 0 0 0.2 0.4 0.6 0.8 1 $_{v}$=0.0 $_{v}$=0.02 $_{v}$=0.03 NL3 $_{v}$=0.03 $_{v}$=0.02 $_{v}$=0.0 FSUGold P=0.11 MeV/fm 3 P=0.331 MeV/fm 3 P=0.11 MeV/fm 3 P=0.276 MeV/fm 3 P=0.11 MeV/fm 3 P=0.210 MeV/fm 3 P=0.11 MeV/fm 3 P=0.209 MeV/fm 3 P=0.11 MeV/fm 3 P=0.266 MeV/fm 3 P=0.11 MeV/fm 3 P=0.303 MeV/fm 3 n p n p p p p p n n n n -0.2 0 0.2 0.4 P (MeV/fm 3 ) 0 0.04 0.08 0.12  (fm$^{-3}$) -0.2 0 0.2 0.4 P (MeV/fm 3 ) NL3 FSUGold  = 0 0.2 0.4 0.6 0.8 1.0  = 0 0.2 0.4 0.6 0.8 1.0 $_{v}$=0.0 $_{v}$=0.03 T=10 MeV FIG. 3: Chemical potential isobars as a function of isospin asymmetry α at temperature T = 10 MeV for NL3 (left panel) and FSUGold (right panel) with different Λ v couplings. The geometrical construction used to obtain the isospin asymme- tries and chemical potentials in the two coexisting phases is also shown. FIG. 2: Pressure as a function of density at temperature T = 10 MeV for various isospin asymmetry α in the original NL3 set [27] with Λ v = 0 . 0 (top panel) and the original FSUGold set [28] with Λ v = 0 . 03 (right panel). The dotted curves refer to unstable single phase while the solid curves refer to stable matter; see text for details. The first inequality indicates mechanical stability which means a system at positive isothermal compressibility re- mains stable at all densities. The second inequality stems from chemical instability which shows that energy is re- quired to change the concentration in a stable system while maintaining temperature and pressure fixed. If one of these conditions get violated, a system with two phases is energetically favorable. The two phase coexistence is governed by the Gibbs’s criteria for equal chemical po- tentials and pressures in the two phases with different densities but at the same temperature: constant at all densities. Finally the system leaves the co- existence region and vaporizes into the low density (gas) phase. Of particular interest here is the symmetry en- ergy effects on the isotherms. It is clearly seen that in contrast to the original NL3 with Λ$_{v}$ = 0, the softer E$_{sym}$ ( ρ ) in the original FSUGold with Λ$_{v}$ = 0 . 03 [17] en- forces the onset of pure liquid phase to a higher density resulting in a wider coexistence region for each asymme- try α . Moreover, the critical pressure P$_{c}$ above which the mixed liquid-gas phase vanishes is seen larger for this soft FSUGold set; a detailed discussion of which is presented below. The details of chemical evolution for the LGP transi- tion is depicted in Fig. 3 where the neutron and proton chemical potentials are shown as a function of isospin asymmetry α at a fixed T = 10 MeV and pressure P = 0 . 11 MeV/fm 3 for the NL3 (left panels) and FSUG- old (right panels) at various Λ$_{v}$ values. As usual, the bare nucleon mass has been subtracted from the chemi- cal potentials. At fixed pressure and Λ$_{v}$, the solutions of the Gibbs conditions (9) and (10) for phase equilibrium form the edges of a rectangle and can be found by geo- metrical construction as shown in Fig. 3. At each Λ$_{v}$, the two different values of α defines the high density liquid phase boundary (with small α = α$_{1}$ ( T, P )) and the low density gas phase boundary (with large α = α$_{2}$ ( T, P )). From the figure it is evident that the symmetry energy Figure 2 shows the pressure as a function of nucleon density at a fixed temperature T = 10 MeV with different values of asymmetry α in the original NL3 and FSUGold sets. Below a critical value of asymmetry α , the pressure is seen (dotted curves) to decrease with density result- ing in negative incompressibility and thereby a mechani- cally unstable system. The stable two-phase (liquid-gas) configuration at each density is obtained from Maxwell construction (solid lines). Analogues to intermediate en- ergy heavy-ion collisions [1, 2] when the hot matter in the high density (liquid) phase expands it enters the coexis- tence LGP where the pressure decreases at a fixed α = 0 for the two-component asymmetric matter. Whereas, for symmetric nuclear matter at α = 0 the pressure remains P $^{L}$( T, ρ $^{L}$) = P $^{G}$( T, ρ $^{G}$) . (10) µ L $_{q}$( T, ρ $^{L}$) = µ G q ( T, ρ $^{G}$) ( q = n, p ) , (9)