Varied phenomenology of models displaying dynamical large-deviation singularities

TL;DR

This paper investigates models of driven random walkers on a lattice, revealing that large-deviation singularities are linked to diverging timescales rather than true phase transitions, with phenomenology depending on driving details.

Contribution

It demonstrates that large-deviation singularities do not always signify phase transitions, highlighting the importance of model specifics and timescale divergence in dynamical phenomenology.

Findings

Large-deviation singularities depend on driving details.

Singularities indicate diverging timescales, not necessarily phase coexistence.

Behavior varies between ergodic and non-ergodic models.

Abstract

Singularities of dynamical large-deviation functions are often interpreted as the signal of a dynamical phase transition and the coexistence of distinct dynamical phases, by analogy with the correspondence between singularities of free energies and equilibrium phase behavior. Here we study models of driven random walkers on a lattice. These models display large-deviation singularities in the limit of large lattice size, but the extent to which each model's phenomenology resembles a phase transition depends on the details of the driving. We also compare the behavior of ergodic and non-ergodic models that present large-deviation singularities. We argue that dynamical large-deviation singularities indicate the divergence of a model timescale, but not necessarily one associated with cooperative behavior or the existence of distinct phases.