Large deviations and ensembles of trajectories in stochastic models

TL;DR

This paper explores how ensembles of trajectories in stochastic models relate to large deviations and physical phenomena, demonstrating generation methods and connections to quantum phase transitions.

Contribution

It introduces a method to generate biased trajectory ensembles using auxiliary stochastic processes and links these ensembles to physical phenomena and quantum phase transitions.

Findings

Biased ensembles can exhibit ferromagnetic ordering.

Auxiliary processes enable direct generation of trajectory ensembles.

Connections established between biased ensembles and quantum phase transitions.

Abstract

We consider ensembles of trajectories associated with large deviations of time-integrated quantities in stochastic models. Motivated by proposals that these ensembles are relevant for physical processes such as shearing and glassy relaxation, we show how they can be generated directly using auxiliary stochastic processes. We illustrate our results using the Glauber-Ising chain, for which biased ensembles of trajectories can exhibit ferromagnetic ordering. We discuss the relation between such biased ensembles and quantum phase transitions.