Response functions near the liquid-liquid critical point of ST2 water

We simulate the ST2 water model for time periods up to 1000 ns, and for four different system sizes, N = 6(3), 7(3), 8(3), and 9(3). We locate the liquid-liquid phase transition line and its critical point in the supercooled region. Near the liquid-liquid phase transition line, we observe that the system continuously flips between the low-density and high-density liquid phases. We analyze the transition line further by calculating two thermodynamic response functions, the isobaric specific heat capacity C-P and the isothermal compressibility K-T. We use two different methods: (i) from fluctuations and (ii) with the relevant thermodynamic derivative. We find that, within the accuracy of our simulations, the maxima of two different response functions occur at the same temperatures. The lines of C-P and K-T maxima below the critical pressure approximate the Widom line which is continuous with the line of first-order transitions in the two-phase region where we observe the phase flipping.