Efficient Computation of Entropy and Other Thermodynamic Properties for Two-Dimensional Systems Using Two-Phase Thermodynamic Model

We present a method based on the two-phase thermodynamic model (2PT) to calculate the entropy and free energy of various molecular systems in two dimensions (2D) using molecular dynamics (MD) simulations. The 2PT method has been used widely to calculate absolute entropy in a variety of molecular systems in three dimensions. When applying the idea to 2D systems, we found that the fluidicity that determines the decomposition of the vibrational density of states (DoS) into a solidlike and a gaslike component needs to be revised. The solid part is treated using quantum statistics, and the gas part is treated as a hard-disk fluid. We validate this method by computing thermodynamic properties of a two-dimensional Lennard-Jones fluid over a range of densities and temperatures and find excellent agreement with these quantities computed from the equation of state. More importantly, this method allows for the calculation of the entropy and free energy of 2D systems efficiently from a single MD trajectory of less than 50 ps; therefore, it can be a new, powerful way of assessing the thermodynamic properties in 2D problems.