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 [F. Jülicher et al., Rev. Mod. Phys. 69, 1269 (1997)]. However, people have recently noticed some apparent exceptions to this principle in systems with spatially varying fluctuations sources [J. Stenhammar et al., Sci. Adv. 2, e1501850 (2016)]. In this talk, I will show how hidden symmetries can prevent these steady currents. I will first show how dilute systems can exhibit detailed blanace with respect to non-Boltzmann steady states, restoring equilibrium. Then, for interacting systems, I will show how effective bulk momentum conservation can also prevent the emergence of ratchet currents. The ratchet principle should thus be amended to state that non-equilibrium systems which violate parity symmetry and momentum conservation generically exhibit steady-state currents.