Semiclassical transport of hadrons with dynamical spectral functions in A + A collisions at SIS/AGS energies

We continue the description of the dynamics of unstable particles within the real-time formulation of nonequilibrium field theory initiated in a previous paper [1]. There we suggest to use Baymʹs phi-functional method in order to achieve approximation schemes with ʹbuilt in" consistency with respect to conservation laws and thermodynamics even in the case of particles with finite damping width. Starting from Kadanoff-Baym equations we discuss a consistent first order gradient approach to transport which preserves the phi-derivable properties. The validity conditions for the resulting quantum four-phase-space kinetic theory are discussed under the perspective to treat particles with broad damping widths. This non-equilibrium dynamics naturally includes all those quantum features already inherent in the corresponding equilibrium limit (e.g. Matsubara formalism) at the same level of phi-derivable approximation. Various collision-term diagrams are discussed including those of higher order which lead to memory effects. As an important novel part we derive a generalized nonequilibrium expression for the kinetic entropy flow, which includes contributions from fluctuations and mass-width effects. In special cases an H-theorem is derived implying that the entropy can only increase with time. Memory effects in the kinetic terms provide contributions to the kinetic entropy flow that in the equilibrium limit recover the famous bosonic type T^3 In T correction to the specific heat in the case of Fermi liquids like Helium-3.