  The formal derivation of Langevin equations (and, equivalently Fokker-Planck
equations) with projection operator techniques of Mori, Zwanzig, Kawasaki and
others apparently not has widely found its way into textbooks. It has been
reproduced dozens of times on the fly with many references to the literature
and without adding much substantially new. Here we follow the tradition, but
strive to produce a self-contained text. Furthermore, we address questions that
naturally arise in the derivation. Among other things the meaning of the
divergence of the Poisson brackets is explained, and the role of nonlinear
damping coefficients is clarified. The derivation relies on classical
mechanics, and encompasses everything one can construct from point particles
and potentials: solids, liquids, liquid crystals, conductors, polymers, systems
with spin-like degrees of freedom ... Einstein relations and Onsager
reciprocity relations come for free.
