A Generalized Einstein Relation for Markovian Friction Coefficients from Molecular Trajectories

TL;DR

This paper introduces a generalized Einstein relation linking friction coefficients with observable correlation functions, enabling more accurate and stable extraction of friction profiles from molecular trajectories compared to traditional methods.

Contribution

It develops a flexible generalized Einstein relation for memory-dependent friction coefficients, improving numerical stability and accuracy in kernel extraction from molecular trajectory data.

Findings

Successfully recovered site-specific friction coefficients from model trajectories.

Achieved improved accuracy over existing Volterra inversion methods.

Demonstrated applicability to a freely diffusing molecular trimer.

Abstract

We present a generalized Einstein relation for the friction coefficients associated with an underlying memory kernel in terms of observable time correlation functions. There is considerable freedom in the correlations involved, and this allows the expression to be tailored to the particular system to achieve numerical stability. We demonstrate this by recovering the site-specific friction coefficients from trajectories of a freely diffusing model trimer, and we show that the accuracy is greatly improved over established Volterra inversion methods for kernel extraction.