A framework for the direct evaluation of large deviations in non-Markovian processes

TL;DR

This paper introduces a versatile framework for simulating non-Markovian stochastic processes and efficiently computing large deviation functions, extending existing cloning methods to systems with long memory.

Contribution

It generalizes the cloning procedure to non-Markovian systems, enabling accurate large deviation evaluations in processes with long memory dependence.

Findings

Validated the method on non-Markovian ion-channel models.

Successfully applied the framework to the Totally Asymmetric Exclusion Process.

Recovered known results using the new approach.

Abstract

We propose a general framework to simulate stochastic trajectories with arbitrarily long memory dependence and efficiently evaluate large deviation functions associated to time-extensive observables. This extends the "cloning" procedure of Giardin\'a et al. [Phys. Rev. Lett. 96, 120603 (2006)] to non-Markovian systems. We demonstrate the validity of this method by testing non-Markovian variants of an ion-channel model and the Totally Asymmetric Exclusion Process, recovering results obtainable by other means.