  Macroscopic fields like electromagnetic, MHD, acoustic or gravitational waves
are usually described by classical wave equations with possible additional
damping terms and coherent sources. The aim of this paper is to develop a
complete macroscopic formalism including random/thermal sources, dissipation
and random scattering of waves by environment. The proposed reduced state of
field (RSF) combines averaged field with the two-point correlation function
called single-particle density matrix. The evolution equations for RSF is
obtained by reduction of the generalized quasi-free dynamical semigroups
describing irreversible evolution of bosonic quantum field and the definition
of RSF's entropy follows from the von Neumann entropy of quantum field states.
The presented formalism can be applied, for example, to superradiance phenomena
and allows to unify the Mueller and Jones calculi in polarization optics.
