New expression of the bulk viscosity

We provide a physical insight into the mechanism of the bulk viscosity ζ and construct a new expression of ζ directly from microscopic information such as the interatomic potential and the pair distribution function. This is an outstanding advantage when compared to the previously proposed formulae in all of which ζ is expressed only in terms of pressure. Among some of the previously proposed formulae, we prove that the Green–Kubo formula and the Heyes formula are both equivalent to our new formula when the pressure in their expressions is described by means of interatomic potentials and pair distribution functions under appropriate conditions. This fact confirms the validity of our formula, which reinforces the aforementioned advantage. We calculate ζ near the triple point of the Lennard–Jones fluid using our formula, the Green–Kubo formula and the Heyes method. The obtained values of ζ are in good agreement with one another.