Strongly correlated electronic states (SCES), that determine the anomalies of physicochemical properties, are well-known for solid materials at low temperatures. According to the mechanism of manifestation their existence can be assumed in biological cells with white spots, which makes us look into this challenging problem in detail. The paper presents its solution through a study of simple models of micellar solutions of ionic surfactants. The process of micelle formation with accompanying liquid-liquid phase transition makes us pay attention to possible anomalies of properties. Therefore the SCES of water micellar solution has been tested by compenstion and cooperative effects; and by small-angle, wide-angle X-ray, dynamic and chiral scattering of electromagnetic radiation. The solution water is represented by ensembles of small nano systems. Therefore, thermal (cavities for micelles 2-6 nm) and quantum (0.2-0.3 nm) fluctuations of water appear in the zone of concentration of micelle formation. Their energy is approximately equal to the H-bond. Contraction (expansion) of water H-bonds network of due to quantum fluctuations on a small scale correlates with the expansion (contraction) of the in the cavities in the micelles H-bonds network due to thermal fluctuations on a large scale. This phenomenon is caused by SСES.