Trajectory reweighting for non-equilibrium steady states

TL;DR

Trajectory reweighting offers a theoretical extension for sampling non-equilibrium steady states, but practical issues limit its effectiveness, suggesting the need for alternative path ensemble methods like PERM.

Contribution

The paper analyzes the limitations of trajectory reweighting in non-equilibrium systems and proposes that path ensemble methods could overcome these challenges.

Findings

Trajectory reweighting faces practical sampling issues in rugged landscapes.

Long trajectories lead to broad weight distributions, hindering effective sampling.

Path ensemble methods like PERM may provide a solution.

Abstract

Modern methods for sampling rugged landscapes in state space mainly rely on knowledge of the relative probabilities of microstates, which is given by the Boltzmann factor for equilibrium systems. In principle, trajectory reweighting provides an elegant way to extend these algorithms to non-equilibrium systems, by numerically calculating the relative weights that can be directly substituted for the Boltzmann factor. We show that trajectory reweighting has many commonalities with Rosenbluth sampling for chain macromolecules, including practical problems which stem from the fact that both are iterated importance sampling schemes: for long trajectories the distribution of trajectory weights becomes very broad and trajectories carrying high weights are infrequently sampled, yet long trajectories are unavoidable in rugged landscapes. For probing the probability landscapes of genetic switches and similar systems, these issues preclude the straightforward use of trajectory reweighting. The analogy to Rosenbluth sampling suggests though that path ensemble methods such as PERM (pruned-enriched Rosenbluth method) could provide a way forward.