Computation of Microcanonical Entropy Differences in Atomistic Computer Simulation

In this work, two alternative methods to compute thermodynamic entropy differences $\Delta S=S(E_2)-S(E_1)$ between two microcanonical states (produced via atomistic computer simulation, either deterministic or stochastic) at total energies $E_1$ y $E_2$ are presented. The first method is straightforward to implement, as it only needs potential energy samples from both simulations; however, it requires that fluctuations of potential energy are similar in magnitude to the energy difference $\Delta E$ between the states. It is therefore best suited for simulations in small systems (hundred of atoms). The second method, based on Bayesian probability and information theory, removes this limitation: it allows the computation of the entropy curve $S(E)$ for a wide range of energies and therefore is a viable alternative to methods such as Wang-Landau Monte Carlo. It is based on inferring the configurational density of states (CDOS) from potential energy samples. A simple model for the CDOS of embedded atom metals is presented and tested in Au and Cu by computing entropy and free energy differences.