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Non-equilibrium transportation of particles through a restricted space (suchas porous media or narrow channels) significantly differs from free space. Witha simple model of two types of particles competing to transport via a passivesingle-lane channel connecting two chemical baths, we find two dynamical modesof transportation -- the dud mode and the ratchet mode. At the ratchet mode,the gradient flow of one type of particle forces the other into a transientanti-equilibrium flow against its gradient. At the dud mode, the two types ofparticles both flow according to their gradients. This counter-intuitivenon-equilibrium effect can be explained by a sloppy gear mechanism. In additionto the anti-gradient flow observed in the ratchet mode, we find that thenon-equilibrium sloppy gear mechanism suppresses the flow of one particle whileallowing the flow for the other. This mechanism provides a general theoreticalframework to explain and design the selective transportation of particles viapassive channels.

Sloppy Gear Mechanism for Coupled Stochastic Transportation: from anti-equilibrium flow to infinite selectivity