Generalised Langevin equation

D only assumes a constant value over times long compared with rc( 10rc), such that (u(O)u(f)), the velocity autocorrelation function, is nearly zero. The diffusion equation is not valid over times < 10rc(i.e. a few picoseconds at least). A better approach would be to use a generalised Langevin equation with a friction coefficient which has a memory and such that the velocity autocorrelation takes 0.5ps to decay to insignificant levels (see Chap. 11) [453]. 

Adelman [530] and Stillman and Freed [531] have discussed the reduction of the generalised Langevin equation to a generalised Fokker— Planck equation, which provides a description of the probability that a molecule has a velocity u at a position r at a time t, given certain initial conditions (see Sect. 3.2.). The generalised Fokker—Planck equation has important differences by comparison with the (Markovian) Fokker— Planck equation (287). However, it has not proved so convenient a vehicle for studies of chemical reactions in solution as the generalised Langevin equation (290). 

As far as the linear generalised Langevin equation of a single macromolecule is concerned, general speculations allow us to write down the form of the final results before the calculations are carried out. The requirements of covariance... 

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