Negative Resistance and Rectification in Brownian Transport

We discuss under what conditions Brownian transport processes can display negative resistance. We prove it cannot occur on 1D spaces like the circle or the line. We construct an entropic ratchet: an explicit two-dimensional model, and its collapse onto a branched 1D backbone, showing negative resistance and rectification as a consequence of a geometric symmetry breaking. We derive an accurate numerical method for solving our 2D model. Finally, we discuss analogies and relevance to biological ion channels, in particular, for channel inactivation and blocking.