New approach to Monte Carlo calculation of the free energy: Method of expanded ensembles

TLDR

The approach’s relevance to quantum statistics via path integral Monte Carlo and other applications is highlighted. The authors propose a new effective Monte Carlo procedure that directly calculates free energy in a single run. The method introduces an expanded‑ensemble partition function that sums canonical partition functions over temperatures with additive factors, and uses a random walk in particle coordinates and temperature space to compute free energy across a wide temperature range, with extensions to ensembles varying particle number or volume. Applying the method to a primitive electrolyte model, the authors demonstrate that the random walk yields free‑energy estimates over a broad temperature range, including low temperatures.

Abstract

We propose a new effective Monte Carlo (MC) procedure for direct calculation of the free energy in a single MC run. The partition function of the expanded ensemble is introduced including a sum of canonical partition functions with a set of temperatures and additive factors (modification). Random walk in the space of both particle coordinates and temperatures provides calculation of free energy in a wide range of T. The method was applied to a primitive model of electrolyte including the region of low temperatures. In similar way other variants of expanded ensembles are constructed (e.g., over the number of particles N or volume V). Its facilities in quantum statistics (path integral Monte Carlo) and some other applications are also discussed.