Beyond the Van Der Waals loop: What can be learned from simulating Lennard-Jones fluids inside the region of phase coexistence

As a rule, mean-field theories applied to a fluid that can undergo a transition from saturated vapor at density ρυ to a liquid at density ρl yield a van der Waals loop. For example, isotherms of the chemical potential μ(T,ρ) as a function of the density ρ at a fixed temperature T less than the critical temperature Tc exhibit a maximum and a minimum. Metastable and unstable parts of the van der Waals loop can be eliminated by the Maxwell construction. Van der Waals loops and the corresponding double minimum potentials are mean-field artifacts. Simulations at fixed μ=μcoex for ρυ