Stoke's efficiency and its stochastic properties
  We study the Stoke's efficiency and its fluctuating properties in the case of a spatial asymmetric ratchet potential with a temporal asymmetric driving force from adiabatic to nonadiabatic regime. Our numerical investigations show that the average Stoke's efficiency and the average current decrease with the frequency of driving. For low frequency of driving, i.e., in the case of an adiabatic regime, we reproduced the analytical results supporting our numerical simulations. By evaluating the probability distribution, $p(\eta_{s})$ for Stoke's efficiency, $\eta_{s}$ we focus on the stochastic properties of Stokes efficiency. We find that in most of the parameter space, fluctuations in $\eta_{s}$ are comparable to or larger than the mean values. In such a situation one has to study the full probability distribution of $\eta_{s}$. With increase in frequency of driving, the distribution becomes multipeaked. At the same time the average Stoke's efficiency decreases with increase in frequency of drive. For high frequency of driving, the distribution develops a peak across zero. Further increase in frequency this peak gets sharper. And finally at sufficiently high frequency we get a strong peak across zero indicating that there is no effective transport in this regime. 
Mamata Sahoo and A. M Jayannavar
cond-mat.stat-mech