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

Reversible to irreversible (R-IR) transitions arise in numerous periodically driven collectively interacting systems that, after a certain number of driving cycles, organize into a reversible state where the particle trajectories repeat during every or every few cycles. On the irreversible side of the transition, the motion is chaotic. R-IR transitions were first systematically studied for periodically sheared dilute colloids, and have now been found in a wide variety of both soft and hard matter periodically driven systems, including amorphous solids, crystals, vortices in type-II superconductors, and magnetic textures. It has been shown that in several of these systems, the transition to a reversible state is an absorbing phase transition with a critical divergence in the organization timescale at the transition. The same systems are capable of storing multiple memories and may exhibit return point memory. We give an overview of R-IR transitions including recent advances in the field and discuss 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. In particular, some likely candidate systems are commensurate-incommensurate states, systems exhibiting hysteresis or avalanches, nonequilibrium pattern forming states, and other systems with absorbing phase transitions. Periodic driving could be applied to hard condensed matter systems to see if organization into reversible states occurs for metal-insulator transitions, transitions could also be examined in dynamical systems where synchronization or phase locking occurs. We also discuss the possibility of using complex periodic driving, such as changing drive directions or using multiple frequencies, to determine whether these systems can still organize to reversible states or retain complex multiple memories. Finally, we describe features of classical and quantum time crystals that could suggest the occurrence of R-IR transitions in these systems.

Automated summary

Reversible to irreversible (R-IR) transitions occur in various periodically driven collective systems. These systems organize into a reversible state after a certain number of driving cycles, where particle trajectories repeat. On the irreversible side, motion is chaotic. R-IR transitions have been extensively studied in different systems, including dilute colloids, amorphous solids, crystals, superconductors, and magnetic textures. The transition to a reversible state is often an absorbing phase transition, with a critical divergence in the organization timescale. These transitions can be applied to a broader range of nonequilibrium systems, such as commensurate-incommensurate states, systems with hysteresis or avalanches, and systems with absorbing phase transitions.