Conventional and generalized efficiencies of flashing and rocking ratchets: Analytical comparison of high-efficiency limits

Abstract

We consider two basic types of Brownian motors which generate directed motion in a periodic asymmetric piecewise-linear potential as a result of random half-period shifts of the potential relief (flashing ratchets) or due to a temporally asymmetric unbiased force applied to the system (rocking ratchets). Analytical relationships have been derived which enable the comparison of the upper limits for the conventional and generalized energy conversion efficiencies in these motors. As found, the increasing amplitude of a sawtooth potential (or the decreasing temperature) makes the conventional efficiency tend to the unity limit faster for a rocking ratchet (in the absence of temporal asymmetry) than for a flashing ratchet. The inverse is true for the generalized efficiency. The potential amplitude being the same, the generalized efficiency is always less than the conventional efficiency. A decreased asymmetry of the potential always results in the reduction of both efficiencies. The temporal asymmetry of an unbiased force has an opposite effect on the conventional and generalized efficiencies: the former rises and the latter drops as the positive signal component becomes shorter in time and larger in amplitude.

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.…”

Ratchet effects of a Brownian particle system with non-Gaussian noise driven by a biharmonic force

“…The theoretical and experimental investigations of ratchet transport of a Brownian particle have attracted much attention in recent years [1][2][3][4][5][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] for its wide range of potential applications. The transport phenomenon appears in many fields, such as in molecular motors, 2,5,[7][8][9][10][11][12] nanotechnologies of biological systems such as ion pumps, [25][26][27] artificial nanopores 28 and cold atoms in optical lattices, 29,30 etc.…”

“…Recently, there have been some extensive discussions shifting from the spatial asymmetry to the temporal asymmetry, for example, the transport effects driven by biharmonic force have been investigated in dissipative rocking ratchets, 3,4 Brownian particle transport effect, 5 the ring laser system, 24 etc. Rozenbaum et al 12 considered two basic types of Brownian motors in a periodic asymmetric piecewise-linear potential and observed the temporal asymmetry has an opposite effect on the conventional and generalized efficiencies in time and in amplitude. The discussion is mainly focused on the theory analysis, the amplitude and the phase difference-induced transport.…”

Performance optimization in two-dimensional Brownian rotary ratchet models

“…with F ≡ (F x , F y ) ≡ f h + f I andF ≡ F − γ Ẋ . The equality (1.5) is derived in [25] based on [30][31][32][33]. Here, we define the long time average of A as A ≡ A(X, Φ t ) ≡ Ttot 0 dt A(X, Φ t )/T tot for T tot Ω −1 , and assume A = A(X, Φ t ) Φ (ergodic hypothesis),…”

“…In one-dimensional ratchet systems in particular, proposals have been made for exact expressions for the efficiency or for models that realize highly efficient performance, e.g., [30,[35][36][37][38]. In the context of maximization of efficiency, although there are various aspects to optimization [39,40], basic approaches may be classified into two types: those that optimize the temporally varying part of the ratchet potential [41][42][43], and those that optimize the static part [30,37]. Experiments relevant to these optimization approaches can be found in [13,14].…”