Intrinsic fractional noise in nanopores: The effect of reservoirs

Fluctuations affect nanoporous transport in complex and intricate ways, making optimization of signal-to-noise in artificial designs challenging. Here we focus on the simplest nanopore system, where non-interacting particles diffuse through a pore separating reservoirs. We find that the concentration difference between both sides (akin to the osmotic pressure drop) exhibits fractional noise in time $t$ with mean square average that grows as $t^{1/2}$. This originates from the diffusive exchange of particles from one region to another. We fully rationalize this effect, with particle simulations and analytic solutions. We further infer the parameters (pore radius, pore thickness) that control this exotic behavior. As a consequence, we show that the number of particles within the pore also exhibits fractional noise. Such fractional noise is responsible for noise spectral density scaling as $1/f^{3/2}$ with frequency $f$, and we quantify its amplitude. Our theoretical approach is applicable to more complex nanoporous systems (for example with adsorption within the pore) and drastically simplifies both particle simulations and analytic calculus.