Equilibration and order in quantum Floquet matter

Equilibrium thermodynamics is characterized by two fundamental ideas: thermalization-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 summarize 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/Floquet time crystal.