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

Nobuko Fuchikami; Shunya Ishioka

doi:10.1117/12.488776

7 May 2003 Directed current in ratchets by pseudo-Gaussian white noise: a seeming paradox from a Langevin equation and an alternative master equation

Nobuko Fuchikami, Shunya Ishioka

Author Affiliations +

Proceedings Volume 5114, Noise in Complex Systems and Stochastic Dynamics; (2003) https://doi.org/10.1117/12.488776
Event: SPIE's First International Symposium on Fluctuations and Noise, 2003, Santa Fe, New Mexico, United States

Abstract

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.

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Nobuko Fuchikami and Shunya Ishioka "Directed current in ratchets by pseudo-Gaussian white noise: a seeming paradox from a Langevin equation and an alternative master equation", Proc. SPIE 5114, Noise in Complex Systems and Stochastic Dynamics, (7 May 2003); https://doi.org/10.1117/12.488776

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