Two approaches toward a high-efficiency flashing ratchet

Abstract

For a flashing ratchet with periodic potentials fluctuating via random shifts of one-half period, a high efficiency is shown to result from two mechanisms. The previously reported one [Yu. A. Makhnovskii, Phys. Rev. E 69, 021102 (2004); V. M. Rozenbaum, JETP Lett. 79, 388 (2004)] is realized in the near-equilibrium region and implies, first, the presence of a high barrier V0 blocking the reverse movement of a Brownian particle and, second, identical, though energy-shifted, portions of the asymmetric flat potential profile on both half periods. We report another mechanism acting far from equilibrium, typical of strongly asymmetric potentials which are shaped identically on both half periods with a large energetic shift DeltaV . The two mechanisms exhibit radically different limiting behavior of the maximum possible efficiency: eta(m) approximately 1-exp (-beta V0 /2) for the former and eta(m) approximately 1-ln (2betaDeltaV) /betaDeltaV for the latter ( beta being the reciprocal temperature in energy units). The flux and the efficiency for a Brownian motor with a piecewise-linear potential are calculated using the transfer matrix method; an exact analytical solution can thus be obtained for an extremely asymmetric sawtooth potential, the simplest example of the second high-efficiency mechanism. As demonstrated, the mechanisms considered are also characteristic of a two-well periodic potential treated in terms of the kinetic approach.