Accurate estimation of dynamical quantities for nonequilibrium nanoscale systems

Fluctuations of dynamical quantities are fundamental and inevitable. For the booming research in nanotech-nology, huge relative fluctuation comes with the reduction of system size, leading to large uncertainty for the estimates of dynamical quantities. Thus, increasing statistical efficiency, i.e., reducing the number of samples required to achieve a given accuracy, is of great significance for accurate estimation. Here we propose a theory as a fundamental solution for such problem by constructing auxiliary path for each real path. The states on auxiliary paths constitute canonical ensemble and share the same macroscopic properties (NVT) with the initial states of the real path. By implementing the theory in molecular dynamics simulations, we obtain a nanoscale Couette flow field with an accuracy of 0.2 mu m/s with relative standard error <0.1. The required number of samples is reduced by 12 orders compared to conventional method. The predicted thermolubric behavior of water sliding on a self-assembled surface is directly validated by experiment under the same velocity. This theory only assumes the system is initially in thermal equilibrium, then driven from that equilibrium by an external perturbation. It could serve as a general approach for extracting the accurate estimate of dynamical quantities from large fluctuations to provide insights on atomic level under experimental conditions, and benefit the studies on mass transport through (biological) nanochannels and fluid film lubrication of nanometer thickness.

Automated summary

Fluctuations are fundamental and inevitable in dynamical quantities. In nanotechnology research, the reduction of system size leads to large relative fluctuation and uncertainty in estimating dynamical quantities. This study proposes a theory that constructs auxiliary paths for each real path, allowing for increased statistical efficiency in accurate estimation. By implementing the theory in molecular dynamics simulations, a nanoscale Couette flow field with high accuracy and reduced sampling requirements is achieved. The predicted thermolubric behavior is validated by experiment, demonstrating the potential of this theory in providing insights on atomic level and benefitting studies on mass transport and fluid film lubrication in nanoscale systems.