Jessica Metzger, MIT

Exceptions to the ratchet theorem and their marginal stability

Breaking time-reversal and left-right symmetries in stochastic dynamics generically leads to steady-state density currents (ratchet currents) – a principle known as the “Ratchet Theorem.” In active matter, a typical example is active particles in an asymmetric potential. An interesting exception is non-interacting self-propelled particles in an asymmetric activity landscape, which does not lead to steady currents. Surprisingly, the ratchet current is restored by including interactions between the particles. We show this exception to the ratchet theorem (among others) possesses a hidden time-reversal symmetry, which is marginally stable. We explain the interaction-induced ratchet current through a mean-field picture.