Multi-point nonequilibrium umbrella sampling and associated fluctuation relations

TL;DR

This paper introduces a straightforward umbrella sampling method for Markov chains to estimate large-deviation rate functions and explores the extended fluctuation relations among different models within a family, including entropy production.

Contribution

It presents a novel umbrella trajectory sampling technique applicable to multiple models and establishes a generalized fluctuation relation for dynamic observables.

Findings

Effective estimation of large-deviation rate functions

Derivation of extended fluctuation relations

Application to entropy production in Markov chains

Abstract

We describe a simple method of umbrella trajectory sampling for Markov chains. The method allows the estimation of large-deviation rate functions, for path-extensive dynamic observables, for an arbitrary number of models within a certain family. The general relationship between probability distributions of dynamic observables of members of this family is an extended fluctuation relation. When the dynamic observable is chosen to be entropy production, members of this family include the forward Markov chain and its time reverse, whose probability distributions are related by the expected simple fluctuation relation.