Two algorithms to compute projected correlation functions in molecular dynamics simulations.

An explicit derivation of the Mori-Zwanzig orthogonal dynamics of observables is presented and leads to two practical algorithms to compute exactly projected observables (e.g., random noise) and projected correlation function (e.g., memory kernel) from a molecular dynamics trajectory. The algorithms are then applied to study the diffusive dynamics of a tagged particle in a Lennard-Jones fluid, the properties of the associated random noise, and a decomposition of the corresponding memory kernel.