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.

Adiabatically slow and adiabatically fast driven ratchets

“…The power output, as usual, reads P out = F A. The power input in this case is found to be [17][18][19]…”

“…A more detailed and rigorous consideration of efficient flashing ratchets is presented in Refs. [18][19][20], where it is shown that the deviation of the maximum efficiency from unity decays exponentially with increasing V 0 at the instantaneous switching of the potential profiles and decays much slower (according to a power law at large V 0 ) when this switching occurs for a finite time interval.…”

“…A detailed analysis of the highly efficient flashing ratchet with half-period-shifted potentials was given in Refs. [18,19]. Thus, both models rely on adiabaticity of the potential change process, which is crucial to avoid energetic losses.…”

Identification of two mechanisms for current production in a biharmonic flashing electron ratchet

“…Here, we identify two parameters, the shape of the potential and the amount of friction on the electron (defined as the ratio of the potential oscillation timescale to the electron relaxation timescale), that, when explored simultaneously over a large parameter space, reveal two modes of ratchet operation that produce current by two different mechanisms. Prior work that explored the effect of shape on the behavior of the ratchet current focused on variations to a single potential [28][29][30][31][32][33][34]; however, while the current from a ratchet of a single shape does show resonances at certain oscillation frequencies [20], examining the frequency dependence of a single shape does not make apparent the transition from under-damped to over-damped ratcheting mechanisms. Identifying this transition, which is only possible when considering the complete space of biharmonic shapes and a large range of friction values, is critical in uncovering physically intuitive behaviors, and relating these behaviors to structural features of this complex system.…”

Directed mechanical motion in nonequilibrium nanosystems: Occurrence conditions and kinematic controllability

“…Much promise is shown by the high‐efficiency types of Brownian motors such as the model with the potential fluctuating by half a period and the so‐called catalytic wheel acting as a molecular pump. Highly efficient conversion of energy input into mechanical energy output in these models is attributed to (i) a high and narrow barrier blocking the reverse motion and (ii) the identical but mutually energy‐shifted potential reliefs on both half‐periods 6, 23–26. Particle transport through biological membranes driven by electric‐field fluctuations is described by the “catalytic wheel” model 26.…”