Persistence in extended dynamical systems

TL;DR

This paper reviews persistence phenomena in extended dynamical systems, focusing on spatial correlations, temporal evolution, and universal behaviors across different models and updating rules.

Contribution

It provides a comprehensive review of persistence in nonequilibrium systems, highlighting the dependence on dynamics and the universality in stochastic models.

Findings

Persistence exhibits universal behavior in directed percolation models.

Spatial correlations in persistent regions evolve distinctly over time.

Different updating rules influence persistence dynamics.

Abstract

Persistence in spatially extended dynamical systems (like coarsening systems and other nonequilibrium systems) is reviewed. We discuss, in particular, the spatial correlations in the persistent regions and their evolution in time in these systems. We discuss the dependence of the persistence behavior on the dynamics of the system and consider the specific example of different updating rules in the temporal evolution of the system. Lastly, we discuss the universal behavior shown by persistence in various stochastic models belonging to the directed percolation universality class.