Stokes efficiency and its stochastic properties

• The notion of the stochastic Stokes efficiency is proposed in a time asymmetric rocked ratchet model.
• The fluctuation in Stokes efficiency dominate its mean value over the larger parameter space of the model.
• The mean Stokes efficiency decreases as we go from adiabatic to nonadiabatic regime.

We study the Stokes 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 Stokes efficiency and the average current decrease with increase in 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(ηs)p(ηs) for Stokes efficiency ηsηs, we focus on the stochastic properties of Stokes efficiency. We find that in most of the parameter space, fluctuations in ηsηs are comparable to or larger than the mean values. In such a situation, one has to study the nature of the full probability distribution of ηsηs. We observe that with increase in frequency of driving, the distribution becomes multipeaked. At the same time, the average Stokes efficiency monotonically decreases with increase in frequency of the drive. For high frequency of driving, the distribution develops a peak at zero. With further increase in frequency of the drive this peak gets sharper. And finally at sufficiently high frequency, we get a strong peak at zero indicating that there is no effective transport in this regime.