Reversible to irreversible transitions in periodic driven many-body systems and future directions for classical and quantum systems

Reversible to irreversible (R-IR) transitions have been found in a wide variety of both soft and hard matter periodically driven collectively interacting systems that, after a certain number of driving cycles, organize into either a reversible state where the particle trajectories repeat during every or every few cycles or into a chaotic motion state. An overview of R-IR transitions including recent advances in the field is followed by a discussion of how the general framework of R-IR transitions could be applied to a much broader class of nonequilibrium systems in which periodic driving occurs, including not only soft and hard condensed matter systems, but also astrophysics, biological systems, and social systems.