Eur. Phys. J. Special Topics 224, 2351-2367 (2015)
https://doi.org/10.1140/epjst/e2015-02416-9

Regular Article

Effective interactions and large deviations in stochastic processes

¹ Department of Physics, University of Bath, Bath BA2 7AY, UK
² Department of Mathematics, King's College London, Strand, London WC2R 2LS, UK

Received: 19 March 2015
Revised: 5 May 2015
Published online: 22 June 2015

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.