Projection techniques in equilibrium statistical mechanics II

Abstract

In an earlier paper, projection techniques were used to make a comparative study of several approaches in non-equilibrium statistical mechanics using a simple model which was inspired by the quantum-mechanical Kac ring. Exact results were derived to show where and how the following approaches differ: the master-equation approach with the Van Hove limit, the Kubo linear response theory, the Peterson non-linear response theory, and exact solutions obtained using the usual projection technique, as well as suggested iterative projection technique. The last approaches brings the projection technique to the mainstream of non-equilibrium methods in so far as reproducibility of old results is concerned. In the literature in the meantime, projection methods have become rather common and productive.