Generalized Einstein Relation for Markovian Friction Coefficients from Molecular Trajectories

Area of Science:

• Statistical Mechanics
• Physical Chemistry
• Computational Chemistry

Background:

• Friction coefficients are crucial for understanding molecular dynamics.
• Extracting friction kernels from simulation data is computationally challenging.
• Existing methods like Volterra inversion can lack numerical stability and accuracy.

Purpose of the Study:

• To present a generalized Einstein relation for friction coefficients.
• To express friction coefficients using observable time correlation functions.
• To improve the accuracy and numerical stability of friction kernel extraction.

Main Methods:

• Developed a generalized Einstein relation connecting friction coefficients to memory kernels.
• Utilized observable time correlation functions for calculations.
• Applied the method to a freely diffusing model trimer to recover site-specific friction coefficients.

Main Results:

• Successfully recovered site-specific friction coefficients from simulation trajectories.
• Demonstrated significantly improved accuracy compared to established Volterra inversion methods.
• Showcased the flexibility in choosing correlations for enhanced numerical stability.

Conclusions:

• The generalized Einstein relation offers a more robust and accurate approach for friction coefficient determination.
• This method provides a valuable tool for analyzing molecular dynamics and transport phenomena.
• The tailored correlation approach enhances the applicability to diverse physical systems.