Non-gaussian, non-markov processes

Abstract

A non-Gaussian treatment of the Mori theory is presented with the intention of explaining the results of recent computer simulations. The Mori equation is replaced by a multi-dimensional Markov process represented by a set of interrelated matrix equations. These are related straight-forwardly to a linear master equation and its Kramers–Moyal expansion. The non-Gaussian nature of the molecular dynamics results may then be represented by truncating the latter at third order, involving an extra operator Γ⁽¹⁾_L. This may be expanded in a matrix over the basis set of Hermite polynomials in terms of which may be represented eigenstates of the usual Fokker–Planck operator Γ⁽⁰⁾_L.