Solution to the plateau problem in the Green-Kubo formula.

Abstract

Transport coefficients appearing in Markovian dynamic equations for coarse-grained variables have microscopic expressions given by Green-Kubo formulas. These formulas may suffer from the well-known plateau problem. The problem arises because the Green-Kubo running integrals decay as the correlation of the coarse-grained variables themselves. The usual solution is to resort to an extreme timescale separation, for which the plateau problem is minor. Within the context of Mori projection operator formulation, we offer an alternative expression for the transport coefficients that is given by a corrected Green-Kubo expression that has no plateau problem by construction. The only assumption is that the Markovian approximation is valid in such a way that transport coefficients can be defined, even in the case that the separation of timescales is not extreme.