Transformations for accelerating mcmc simulations with broken ergodicity

A new approach for overcoming broken ergodicity in Markov Chain Monte Carlo (MCMC) simulations of complex systems is described. The problem of broken ergodicity is often present in complex systems due to the presence of deep "energy wells" in the energy landscape. These energy wells inhibit the efficient sampling of system states by the metropolis algorithm thereby making estimation of the Boltzmann partition function (BPF) more difficult. The approach described here uses transformation functions to create a family of modified or smoothed energy landscapes. This permits the metropolis algorithm and the MCMC approach to sample system states in a way that leads to accurate estimates of a modified BPF (mBPF). Theoretical results show how it is then possible to extrapolate from this mBPF to the BPF value associated with the original landscape with a small absolute error. Computational examples are provided.