Directed current in ratchets by pseuto-gaussian white noise: a seeming paradox from a Langevin equation and an alternative master equation

摘要

Symmetric white Poissonian shot noise with Gaussian distributed amplitudes is shown from an overdamped Langevin equation to induce directed motion of ratchets. The noise becomes white Gaussian in the limit λ → ∞, where λ is the average number of the delta pulses per unit time. The current tends to zero as 1/λ → 0, which agrees with the fact that the directed motion cannot be induced by the thermal noise alone. However, a finite value of 1/λ yields a finite value of the current no matter how small the former may be. Since 1/λ cannot be zero physically, this is a seeming contradiction of the second law of thermodynamics, which originates from the Langevin equation. We discuss this point from an alternative master equation without assuming the Langevin equation.