Revisiting the Ratchet Principle: When Hidden Conservation Laws Prevent Directed Currents in Stochastic Systems

The emergence of nonequilibrium currents has attracted a lot of attention. The "ratchet principle" identifies the violation of any form of parity and time-reversal symmetries as the necessary conditions for the emergence of such currents. Here we study active and passive systems with asymmetric spatially varying fluctuation sources that nevertheless remain flux free. For non-interacting systems, we show that a hidden time-reversal symmetry forbids the emergence of steady currents. At higher densities, pairwise forces break this symmetry but an emergent conservation law for the momentum field may nevertheless prevent steady currents. We show how the presence of this conservation law can be tested analytically and characterize the onset of ratchet currents in its absence. Our results show that the ratchet principle should be refined to also preclude bulk momentum conservation.