An effective one-dimensional approach to calculating mean first passage time in multi-dimensional potentials

Area of Science:

• Chemical Physics
• Statistical Mechanics
• Physical Chemistry

Background:

• Thermally activated escape processes are fundamental in various scientific fields.
• Calculating the mean first-passage time (MFPT) is essential for understanding these processes.
• Exact MFPT formulas are unavailable in multi-dimensional systems, necessitating approximations like Langer's formula.

Purpose of the Study:

• To develop a more accurate method for calculating MFPT in multi-dimensional potentials.
• To improve upon Langer's formula, a multi-dimensional generalization of Kramers's formula.
• To investigate the role of the potential of mean force (PMF) in MFPT calculations.

Main Methods:

• Utilizing the potential of mean force (PMF) within the exact one-dimensional MFPT expression.
• Comparing the developed model's predictions with Brownian dynamics simulations.
• Analyzing the influence of potential landscape characteristics on escape dynamics.

Main Results:

• The proposed model demonstrates improved agreement with Brownian dynamics simulations compared to Langer's formula.
• Significant enhancements in accuracy are observed for systems with small energy barriers.
• Discrepancies arise when the potential is less confining along the escape direction.
• The optimal direction for PMF evaluation deviates from the unstable mode at the saddle point.

Conclusions:

• The novel approach using PMF in the 1D MFPT expression offers a more accurate prediction of escape rates.
• This method provides substantial improvements over Langer's theory, especially for low energy barriers.
• The findings suggest a re-evaluation of the optimal reaction coordinate for escape processes in complex potentials.