What does a large deviation look like?

TL;DR

This paper explores the nature of large deviations in systems by deriving the time evolution of rare, non-typical trajectories that cause significant deviations from average behavior.

Contribution

It introduces a method to analyze the time dynamics of rare events in large deviation theory, providing new insights into their evolution.

Findings

Derived the time evolution equations for rare trajectories

Enhanced understanding of how deviations develop over time

Provided a framework for studying non-typical system behaviors

Abstract

Large deviation theory quantifies the occurence of events that deviate from the average behavior of a system. Such events arise from non-typical trajectories of the dynamics. In this note we derive the time evolution of these rare trajectories.