Stochastic dynamics: reducing degrees of freedom

Abstract

Distinguishing relevant degrees of freedom Often the interest in the behavior of large molecular systems concerns global behavior on longer time scales rather than the short-time details of local dynamics. Unfortunately, the interesting time scales and system sizes are often (far) beyond what is attainable by detailed molecular dynamics simulations. In particular, macromolecular structural relaxation (crystallization from the melt, conformational changes, polyelectrolyte condensation, protein folding, microphase separation) easily extends into the seconds range and longer. It would be desirable to simplify dynamical simulations in such a way that the “interesting” behavior is well reproduced, and in a much more efficient manner, even if this goes at the expense of “uninteresting” details. Thus we would like to reduce the number of degrees of freedom that are explicitly treated in the dynamics, but in such a way that the accuracy of global and long-time behavior is retained as much as possible. All approaches of this type fall under the heading of coarse graining , although this term is often used in a more specific sense for models that average over local details. The relevant degrees of freedom may then either be the cartesian coordinates of special particles that represent a spatial average (the superatom approach , treated in Section 8.4), or they may be densities on a grid, defined with a certain spatial resolution. The latter type of coarse graining is treated in Chapter 9 and leads to mesoscopic continuum dynamics , treated in Chapter 10.