Large deviations and ensembles of trajectories in stochastic models

Understand

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.