On the acceptance probability of replica-exchange Monte Carlo trials

TLDR

The paper analyzes the average acceptance probability of exchange trials in parallel‑tempering Monte Carlo simulations. The authors derive analytical expressions for the acceptance probability, linking it to entropy differences and energy‑distribution overlap, and provide asymptotic forms for large systems. The derived expressions agree quantitatively with simulation results, and Gaussian approximations of energy distributions are shown to be inadequate.

Abstract

An analysis is presented of the average probability of accepting an exchange trial in the parallel-tempering Monte Carlo molecular simulation method. Arguments are given that this quantity should be related to the entropy difference between the phases, and results from simulations of a simple Lennard-Jones system are presented to support this argument qualitatively. Another analysis based on the energy distributions of a replica pair is presented, and an exact expression for the trial-move acceptance probability in terms of the overlap of these distributions is derived. A more detailed expression is presented using an approximation of constant heat capacity, and an asymptotic form for this result, good for large system sizes, is reported. The detailed analyses are in quantitative agreement with the simulation data. It is further shown that treatment of the energy distributions as Gaussians is an inappropriate way to analyze the acceptance probability.