The generalized Langevin equation

Abstract

The simple Langevin equation describes a process which is both Markovian and Gaussian. A generalization of the Langevin equation allows us to deal with processes which are projections of n-dimensional Gaussian- Markov processes. The results are formally equivalent to generalizations proposed by Kubo in 1966 provided the second fluctuation-dissipation theorem is assumed true. Molecular motion in liquids is discussed in general terms and it is concluded that these generalizations of the Langevin equation are not likely to be successful.