The “2-nodes-2-links” model of stochastic transitions between two states along two possible paths. Different paths are characterized by the values of the corresponding potential barriers W 1 and W 2. The two states are characterized by the values of their well depths, E 1 and E 2. Periodic modulation of these parameters leads to appearance of a nonzero, on average, circulating current in the preferred (clockwise or counterclockwise) direction.
Two steps (a) W 1 < W 1 and (b) W 1 > W 2. At the low-temperature limit, the effective model is a diffusion on a tree graph that consist only of one link and two sites.
A graph with 2 nodes and N links. Nodes are characterized by energies E 1 and E 2. There are two sets of links that are permanently degenerate, so that links with numbers 1,…M have the same barrier size W 2, and the links with numbers M + 1, …N have barrier size W 1.
Effective kinetic models that describe evolution of the system in Fig. 3 in the limit of low temperature for (a) the case of W 1 < W 2 and (b) the case of W 1 > W 2.
Contour of integration.
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