  Effects of the propagation of particles, which have a finite life-time and an
according width in their mass spectrum, are discussed in the context of
transport description. First, the importance of coherence effects
(Landau-Pomeranchuk-Migdal effect) on production and absorption of field quanta
in non-equilibrium dense matter is considered. It is shown that classical
diffusion and Langevin results correspond to re-summation of certain
field-theory diagrams formulated in terms of full non-equilibrium Green's
functions. Then the general properties of broad resonances in dense and hot
systems are discussed in the framework of a self-consistent and conserving
Phi-derivable method of Baym at the examples of the rho-meson in hadronic
matter and the pion in dilute nuclear matter. Further we address the problem of
a transport description that properly accounts for the damping width of the
particles. The Phi-derivable method generalized to the real-time contour
provides a self-consistent and conserving kinetic scheme. We derive a
generalized expression for the non-equilibrium kinetic entropy flow, which
includes corrections from fluctuations and mass-width effects. In special cases
an H-theorem is proved. Memory effects in collision terms give contributions to
the kinetic entropy flow that in the Fermi-liquid case recover the famous
bosonic type T^3 ln T correction to the specific heat of liquid Helium-3. At
the example of the pion-condensate phase transition in dense nuclear matter we
demonstrate important part played by the width effects within the quantum
transport.
