Evidently, the phase coexistence curves (cf. figures) are of fundamental importance to characterize the Lennard-Jones potential. Furthermore, Brown's characteristic curves yield an illustrative description of essential features of the Lennard-Jones potential. Brown's characteristic curves are defined as curves on which a certain thermodynamic property of the substance matches that of an ideal gas. For a real fluid, Z and its derivatives can match the values of the ideal gas for special T , ρ ρ combinations only as a result of Gibbs' phase rule. The resulting points collectively constitute a characteristic curve. Four main characteristic curves are defined: One 0th-order (named Zeno curve) and three 1st-order curves (named Amagat, Boyle, and Charles curve). The characteristic curve are required to have a negative or zero curvature throughout and a single maximum in a double-logarithmic pressure-temperature diagram. Furthermore, Brown's characteristic curves and the virial coefficients are directly linked in the limit of the ideal gas and are therefore known exactly at ρ ρ → → 0 . Both computer simulation results and equation of state results have been reported in the literature for the Lennard-Jones potential.