Dynamics of coarse grained variables I. Exact results

The Mori scheme for dealing with the description for the time evolution of a many body system towards its equilibrium state is used to construct a set of coarse grained or mesoscopic variables whose dynamics is uniquely connected with the corresponding microscopic dynamic operator. Also, the transport equations governing the time evolution of the macroscopic variables are derived, and the results shown to be equivalent to more familiar ones. The connection between these schemes and more intuitive ones which have served as basis to propose time evolution equations for “gross variables”, in particular in mode-mode coupling theories, is also pointed out.