Computing stationary distributions in equilibrium and non-equilibrium systems with Forward Flux Sampling

TL;DR

This paper introduces a novel method using Forward Flux Sampling to efficiently compute stationary distributions in both equilibrium and non-equilibrium systems, linking rate constants directly to distributions without separate calculations.

Contribution

The method provides a direct way to obtain stationary distributions from rate constants in complex systems, simplifying analysis of activated processes.

Findings

Successfully applied to non-equilibrium rare events

Effective in nucleation in 2D Ising model

Used for genetic switch flipping

Abstract

We present a method for computing stationary distributions for activated processes in equilibrium and non-equilibrium systems using Forward Flux Sampling (FFS). In this method, the stationary distributions are obtained directly from the rate constant calculations for the forward and backward reactions; there is no need to perform separate calculations for the stationary distribution and the rate constant. We apply the method to the non-equilibrium rare event problem proposed by Maier and Stein, to nucleation in a 2-dimensional Ising system, and to the flipping of a genetic switch.