An Exact Multiple-Time-Step Variational Formulation for the Committor and the Transition Rate

Area of Science:

• Chemical Physics
• Computational Chemistry
• Statistical Mechanics

Background:

• The committor probability is essential for analyzing transitions between stable states in dynamical systems.
• Current estimation methods using lag time can introduce bias in practical applications.
• Accurate estimation of transition rates is vital for understanding reaction mechanisms and kinetics.

Purpose of the Study:

• To develop a novel expression for estimating the committor and transition rate that is minimized by the exact committor at any lag time.
• To reduce bias and improve the accuracy of committor and transition rate estimations.
• To provide a more robust method for analyzing chemical dynamics and kinetics.

Main Methods:

• Introduced an alternative expression for the committor and transition rate estimation.
• Utilized stopping times (entry times into stable states) instead of lag times.
• Performed numerical tests on benchmark systems to validate the new method.

Main Results:

• The new expression is minimized by the exact committor at any lag time, unlike existing methods.
• Committor and transition rate estimates showed significantly reduced sensitivity to the choice of lag time.
• Combining results from two lag times further improved transition rate accuracy.

Conclusions:

• The proposed method offers a less biased and more accurate estimation of committor probability and transition rates.
• The use of stopping times provides a more reliable approach for analyzing complex dynamical systems.
• The findings have implications for computational chemistry, chemical physics, and statistical mechanics.