Effective interactions and large deviations in stochastic processes

TL;DR

This paper explores how effective interactions in complex stochastic systems relate to large deviations, highlighting their theoretical connections and potential physical applications.

Contribution

It provides a comprehensive review of the relationship between effective interactions, large deviations, and optimal control in many-body systems.

Findings

Effective interactions can induce specific rare events in stochastic systems.

Connections between large deviations at level 2.5 and optimal control are elucidated.

Potential physical applications of variational principles are discussed.

Abstract

We discuss the relationships between large deviations in stochastic systems, and "effective interactions" that induce particular rare events. We focus on the nature of these effective interactions in physical systems with many interacting degrees of freedom, which we illustrate by reviewing several recent studies. We describe the connections between effective interactions, large deviations at "level 2.5", and the theory of optimal control. Finally, we discuss possible physical applications of variational results associated with those theories.