Bringing discrete-time Langevin splitting methods into agreement with thermodynamics

Abstract

In light of the recently published complete set of statistically correct GJ methods for discrete-time thermodynamics, we revise the differential operator splitting method for the Langevin equation in order to comply with the basic GJ thermodynamic sampling features, namely the Boltzmann distribution and Einstein diffusion, in linear systems. This revision, which is based on the introduction of time scaling along with flexibility of a discrete-time velocity attenuation parameter, provides a direct link between the ABO splitting formalism and the GJ methods. This link brings about the conclusion that any GJ method has