  The existence of net flux across the nanochannels under the asymmetrical
static 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 the
thermodynamics holds, and whether the observations result from the numerical
artifacts. Here we use a simple mathematics to demonstrate the existence of
biased-directional transportation (net flux across the channel) in those
asymmetrical nanoscale systems at room temperature, at least in the MD
simulations. We find that the key to the existence of biased-directional
transportation is that the thermal noise is not white anymore at nanoscale; it
includes the color noise with an autocorrelation time length (for MD
simulation, this length is of ~10 ps).
