Reconstructing free-energy landscapes for nonequilibrium periodic potentials

Abstract

We present a method for reconstructing the free-energy landscape of overdamped Brownian motion on a tilted periodic potential. Our approach exploits the periodicity of the system by using the k-space form of the Smoluchowski equation and we employ an iterative approach to determine the nonequilibrium tilt. We reconstruct landscapes for a number of example potentials to show the applicability of the method to both deep and shallow wells and near-to- and far-from-equilibrium regimes. The method converges logarithmically with the number of Fourier terms in the potential.