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Isosbestic (equal absorption) points in the IR and NIR spectra of liquid water are a well known feature and they witness the existence of two populations of oscillators in the probed system. Despite it is a well known experimental fact, in the mainstream molecular dynamics approach the proposed theoretical explanations for it are not able to elucidate which is the physical reason why such a cut off frequency (at the isosbestic point) does exist. We investigate pure Milli-Q water on increasing the temperature in the vis-NIR range (400-2500 nm). We specifically payed attention to the first overtone region (1300-1600 nm) of the OH-bond stretching-mode where an isosbestic point has been observed. A second derivative analysis clearly shows two modes, which can be assigned to water molecules involved in different hydrogen bonding configurations whose relative abundance is controlled by the temperature. We have also observed that the ratio of these modes follows a van't Hoff behavior supporting that their energy difference (energy gap) is independent on the temperature. Furthermore, a log-log plot shows a scale invariance of the population ratio with respect to the perturbation (temperature), confirming the existence of a long range correlated dynamics in the liquid. We show that the two phases differences between energy and entropy estimated from the experimental data can be compared with the predictions of Quantum Electro Dynamics (QED) showing a remarkable agreement.