Large deviations of the dynamical activity in the East model: analysing structure in biased trajectories

TL;DR

This paper investigates large deviations in the dynamical activity of the East model by biasing the system, revealing hierarchical responses and effective interactions that resemble equilibrium behavior at different scales.

Contribution

It introduces a novel analysis of biased trajectories in the East model, combining numerical, linear response, and variational methods to uncover effective interactions across biases.

Findings

Hierarchy of responses to bias at different scales

Quasi-equilibrium behavior on short length scales

Deviations from equilibrium on large length scales

Abstract

We consider large deviations of the dynamical activity in the East model. We bias this system to larger than average activity and investigate the structure that emerges. To best characterise this structure, we exploit the fact that there are effective interactions that would reproduce the same behaviour in an equilibrium system. We combine numerical results with linear response theory and variational estimates of these effective interactions, giving the first insights into such interactions in a many-body system, across a wide range of biases. The system exhibits a hierarchy of responses to the bias, remaining quasi-equilibrated on short length scales, but deviating far from equilibrium on large length scales. We discuss the connection between this hierarchy and the hierarchical aging behaviour of the system.