Exceptions to the Ratchet Principle: Inhomogeneous Fluctuations with and without Rectification

The "ratchet principle" is one of the few generic results that hold outside thermal equilibrium. It states that non-equilibrium systems which violate parity symmetry generically exhibit steady-state currents. This has proven extremely useful in explaining many non-equilibrium transport processes, such as the motion of dynein and kinesin along microtubules in the cell. However, people have recently noticed some apparent exceptions to this principle. In this talk, I will show that the reason for these exceptions is an emergent bulk momentum conservation which must also be broken to produce a ratchet current. As a result, the ratchet principle should be amended accordingly.