Relation between the two body entropy and the relaxation time in supercooled water

The two-body excess entropy of supercooled water is calculated from the radial distribution functions obtained from computer simulation of the TIP4P model for different densities upon supercooling. This quantity is considered in connection with the relaxation time of the self intermediate scattering function. The relaxation time shows a mode coupling theory (MCT) behavior in the region of mild supercooling and a strong behavior in the deep supercooled region. We find here that the two-body entropy is connected to the relaxation time and shows a logarithmic behavior with an apparent asymptotic divergence at the mode coupling crossover temperature. There is also evidence of a change in behavior of the two-body entropy upon crossing from the fragile (hopping-free) state to the strong (hopping-dominated) state of supercooled water, and the relation that connects the two-body entropy and the relxation time in the MCT region no longer holds.