Generalized Einstein Relation for Markovian Friction Coefficients from Molecular Trajectories

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.