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The existence of net flux across the nanochannels under the asymmetricalstatic electric fields obtained at room temperature from molecular dynamics(MD) simulations [Nat. Nanotechnol. 2, 709 (2007); Phys. Rev. Lett. 101, 064502(2008)] has been extensively queried on whether the second law of thethermodynamics holds, and whether the observations result from the numericalartifacts. Here we use a simple mathematics to demonstrate the existence ofbiased-directional transportation (net flux across the channel) in thoseasymmetrical nanoscale systems at room temperature, at least in the MDsimulations. We find that the key to the existence of biased-directionaltransportation is that the thermal noise is not white anymore at nanoscale; itincludes the color noise with an autocorrelation time length (for MDsimulation, this length is of ~10 ps).

Demonstration of the existence of biased transportation in the  asymmetric nanoscale systems induced by thermal noise from a simple  mathematics perspective