Two-time thermal Green's functions for commuting dynamical variables

Equations are obtained for the two-time commutator Green's functions that apply directly in the case of dynamical variables described by commuting operators such as the particle number density, energy density, etc., and also in the case of operators whose averaged commutators may vanish. For the commutator Green' s function describing the fluctuations of the particle number density a closed nonlinear equation is obtained which is valid in both the hydrodynamic region and the weak interaction limit.