Equilibration and Order in Quantum Floquet Matter

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.