# Stationary ordered non-equilibrium states of long-range interacting systems

## TL;DR

This paper demonstrates that long-range interacting systems can exhibit strictly stationary non-equilibrium states with ordered structures when subjected to specific perturbations, challenging the typical relaxation to thermodynamic equilibrium.

## Contribution

It introduces a method to induce strictly stationary non-equilibrium states in long-range systems using finite-time perturbations, even in harmonic potentials.

## Key findings

- Existence of strictly stationary non-equilibrium states after perturbation.
- States characterized by ordered microscopic phase space structures.
- Heuristic predictions align with observed properties of these states.

## Abstract

Long-range interacting Hamiltonian systems are believed to relax generically towards non-equilibrium states called "quasi-stationary" because they evolve towards thermodynamic equilibrium very slowly, on a time-scale diverging with particle number. We show here that, by applying a suitable perturbation operator for a finite time interval, we obtain, in a family of long-range systems, non-equilibrium states which appear to be strictly stationary. They exist even in the case of a harmonic potential, and are characterised by an ordered microscopic phase space structure. We give some simple heuristic arguments which predict reasonably well some properties of these states.