Equilibrium free energies from non-equilibrium metadynamics

TL;DR

This paper introduces a new formalism to convert history-dependent metadynamics into a Markovian process, enabling unbiased free energy estimation and error analysis, with applications to other stochastic methods.

Contribution

A novel formalism that maps history-dependent metadynamics to a Markovian process, allowing accurate free energy reconstruction and error quantification.

Findings

Reconstructed free energy is unbiased

Derived an analytical error expression

Applicable to other stochastic sampling methods

Abstract

In this paper we propose a new formalism to map history-dependent metadynamics in a Markovian process. We apply this formalism to a model Langevin dynamics and determine the equilibrium distribution of a collection of simulations. We demonstrate that the reconstructed free energy is an unbiased estimate of the underlying free energy and analytically derive an expression for the error. The present results can be applied to other history-dependent stochastic processes such as Wang-Landau sampling.