Large deviations in the presence of cooperativity and slow dynamics

TL;DR

This paper investigates how large deviations in simple two-state models are affected by cooperativity and slow dynamics, revealing singularities that resemble phase transitions in dynamical systems.

Contribution

It introduces a formalism to analyze intermittency models, showing how singularities relate to symmetry breaking and phase transition analogs in dynamical large deviations.

Findings

Singularities occur with cooperative switching or slow timescales.

Symmetry breaking leads to a change in the large-deviation rate function.

Singularities can indicate dynamical phase transitions, but not always.

Abstract

We study simple models of intermittency, involving switching between two states, within the dynamical large-deviation formalism. Singularities appear in the formalism when switching is cooperative, or when its basic timescale diverges. In the first case the unbiased trajectory distribution undergoes a symmetry breaking, leading to a change of shape of the large-deviation rate function for a particular dynamical observable. In the second case the symmetry of the unbiased trajectory distribution remains unbroken. Comparison of these models suggests that singularities of the dynamical large-deviation formalism can signal the dynamical equivalent of an equilibrium phase transition, but do not necessarily do so.