Simulation of large deviation functions using population dynamics

TL;DR

This paper provides a pedagogical overview of population dynamics methods for simulating large deviation functions in dynamical systems, covering both discrete and continuous time processes and their modifications for static observables.

Contribution

It introduces and explains recent population dynamics techniques for large deviation function simulations, including adaptations for static observables and intermediate times.

Findings

Reviewed methods for discrete and continuous time processes

Explained modifications for static observables

Outlined approaches for intermediate time analysis

Abstract

In these notes we present a pedagogical account of the population dynamics methods recently introduced to simulate large deviation functions of dynamical observables in and out of equilibrium. After a brief introduction on large deviation functions and their simulations, we review the method of Giardin\`a \emph{et al.} for discrete time processes and that of Lecomte \emph{et al.} for the continuous time counterpart. Last we explain how these methods can be modified to handle static observables and extract information about intermediate times.