Generalized Langevin Equations and non-Markovian Fokker-Planck Equations for Molecular Systems
Eric Darve (Stanford)


Modeling molecular systems is often very expensive because of the large number of degrees of freedom, such as all the coordinates of the atoms, which are required to describe the system and because of the presence of multiple time scales (femtosecond to millisecond). This often results in significant computational costs. One approach to address this issue is to formulate stochastic differential equations or Fokker-Planck equations in terms of a small number of resolved variables, which can be order parameters or reaction coordinates. In particular, such methods can predict slow reaction rates which are beyond the time scales which can be resolved using direct molecular dynamics. We will present new techniques to calculate such equations based on the Mori-Zwanzig projection formalism. Numerical examples from benchmark problems to solvated proteins will be presented.