Validating the diffusion approximation through conditional entropies

摘要

The diffusion approximation replaces a real transport dynamics by an approximate stochastic Markov process. It is proposed that, when both dynamics have invariant measures, the conditional entropy of the invariant measure of the real dynamics with respect to the invariant measure of the Markov process be used to assess quantitatively the validity of the approximation. This proposal is tested on particle transport; the diffusion approximation is found to be quite robust, valid for an unexpectedly large range of mass ratios between the solvent and the Brownian particle.