Accurate estimation of dynamical quantities for nonequilibrium nanoscale systems

Area of Science:

• Nanotechnology
• Statistical Mechanics
• Computational Physics

Background:

• Large relative fluctuations in nanoscale systems lead to significant uncertainty in dynamical quantity estimations.
• Increasing statistical efficiency is crucial for accurate measurements in nanotechnology research.
• Conventional methods struggle with the high uncertainty inherent in small-scale systems.

Purpose of the Study:

• To develop a fundamental theory for accurate estimation of dynamical quantities in systems with large fluctuations.
• To enhance statistical efficiency in molecular dynamics simulations.
• To provide a general approach for extracting reliable data from noisy nanoscale systems.

Main Methods:

• Proposed a theory constructing auxiliary paths for each real path.
• Auxiliary paths' states form a canonical ensemble sharing macroscopic properties (NVT) with initial states.
• Implemented the theory in molecular dynamics simulations for nanoscale Couette flow.

Main Results:

• Achieved nanoscale Couette flow field accuracy of 0.2μm/s with relative standard error <0.1.
• Reduced the required number of samples by 12 orders of magnitude compared to conventional methods.
• Experimentally validated the predicted thermolubric behavior of water on a self-assembled surface.

Conclusions:

• The proposed theory offers a fundamental solution for accurate estimation of dynamical quantities despite large fluctuations.
• Applicable to systems initially in thermal equilibrium and driven by external perturbations.
• Potential applications in mass transport studies, nanochannel research, and nanometer-thick fluid film lubrication.