(86j) Entropy Calculation from Molecular Dynamics Simulation

In classical molecular dynamics (MD) simulation, certain thermodynamic properties, including temperature, pressure and internal energy can be computed in a routine matter during the course of the simulation. Entropy and properties such as the Helmholtz free energy or the chemical potential, which depend on entropy, require significantly more sophisticated approaches to quantitatively evaluate. The ultimate objective of this work is to develop a software module for LAMMPS or other classical MD simulator from which the entropy can be calculated with an effort on par to that of other thermodynamic properties. The approach to this problem is to develop a theoretical expression for excess entropy as a universal functional of the radial distribution function (RDF), which can be routinely calculated from an MD simulation. The functional builds upon the modified Kirkwood entropy in the fluid phase and a local approximation to the harmonic crystal in the solid phase. Five materials with vastly different interaction potentials are simulated across solid and fluid phases from 1 K to 10⁷ K. The standard for entropy, by which the validity of the entropy functional is judged, is obtained from conventional thermodynamic integration over this temperature range. Comparison of the functional used to reproduce the entropy standard for the five materials provides insight into the requirements for universality of the functional. Solutions to address numerical challenges to the robust and accessible implementation of the entropy calculation are shared.