# Equilibration and Order in Quantum Floquet Matter

## TL;DR

This paper reviews recent advances in understanding how periodically driven quantum systems, known as Floquet systems, can exhibit unique non-equilibrium phases like Floquet time crystals, extending thermodynamic concepts beyond equilibrium.

## Contribution

It summarizes recent progress in generalizing thermodynamic ideas to Floquet quantum systems, highlighting the discovery of novel non-equilibrium phases.

## Key findings

- Identification of new Floquet phases such as the $f ext{pi}$-spin glass
- Existence of Floquet time crystals only out of equilibrium
- Extension of thermodynamic principles to driven quantum systems

## Abstract

Equilibrium theormodynamics is characterized by two fundamental ideas: thermalisation--that systems approach a late time thermal state; and phase structure--that thermal states exhibit singular changes as various parameters characterizing the system are changed. We summarise recent progress that has established generalizations of these ideas to periodically driven, or Floquet, closed quantum systems. This has resulted in the discovery of entirely new phases which exist only out of equilibrium, such as the $\pi$-spin glass or Floquet time crystal.