Entropy and thermalization of particles in liquids

We describe the entropy of liquids in the context of kinetic theory of dense gases. In the equilibrium regime the statistical entropy has an explicit dependence of the pair correlation function. In order to test the entropy functional, we use the Morse potential to reproduce experimental pair correlation functions of liquid sodium, using the molecular dynamics technique. With this information, we can compare the theoretical entropy with experimental thermodynamic data. On the other hand, from the nonequilibrium point of view, we discuss the entropy-increase-law analyzing the entropy balance equation. The entropy production due to the molecular diffusion processes displays an upper bound which is proportional to the so-called Fisher information. In the regime at which the one-particle distribution function only depends on particles momentum and time, we show that the factor of proportionality which appears in the upper bound is essentially the time integral of the force autocorrelation function between par...