Out-of-equilibrium states as statistical equilibria of an effective dynamics

TL;DR

This paper demonstrates that out-of-equilibrium coherent structures in long-range interacting systems can be understood as statistical equilibria of an effective averaged dynamics, providing insights into complex systems like fluids and gravitational systems.

Contribution

It introduces a method to interpret non-equilibrium structures as equilibria of an effective dynamics derived via averaging, applicable to various long-range interacting systems.

Findings

Non-equilibrium structures correspond to statistical equilibria.

Effective dynamics can be derived using averaging techniques.

The behavior may serve as a prototype for more complex systems.

Abstract

We study the formation of coherent structures in a system with long-range interactions where particles moving on a circle interact through a repulsive cosine potential. Non equilibrium structures are shown to correspond to statistical equilibria of an effective dynamics, which is derived using averaging techniques. This simple behavior might be a prototype of others observed in more complicated systems with long-range interactions, like two-dimensional incompressible fluids or self-gravitating systems.