Resonance transport and kinetic entropy

Abstract

Within the real-time formulation of non-equilibrium field theory generalized transport equations are derived avoiding the standard quasiparticle approximation. They permit to include unstable particles into the transport scheme. In order to achieve a self-consistent, conserving and thermodynamically consistent description, we generalize the Baym's Φ-functional method to genuine non-equilibrium processes. This scheme may be closed at any desired loop order of the diagrams of the functional Φ this way defining a consistent effective theory. By means of a first-order gradient approximation the corresponding Kadanoff-Baym equations are converted into a set of coupled equations. This set consists of a time-irreversible generalized kinetic equation for the slowly varying space-time part of the phase-space distributions and a retarded equation, which provides the fast micro-scale dynamics represented by the four-momentum part of the distributions. Thereby, no constraint to the mass shell of the particles is required any further and the corresponding spectral mass distributions are treated dynamically. The description naturally includes all those quantum features already inherent in the corresponding equilibrium limit (Matsubara formalism). Memory effects appearing in collision term diagrams of higher order are discussed. The variational properties of Φ-functional permit to 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 can be demonstrated implying that the entropy can only increase with time. Memory effects in the kinetic terms provide corrections to the kinetic entropy flow that in equilibrium limit recover the famous bosonic type T 3 ln T correction to the specific heat of Fermi liquids like Helium-3.

Hadron liquid with a small baryon chemical potential at finite temperature

“…[4]. The expression for the entropy is as follows This way one may recover all necessary thermodynamic characteristics of the system.…”

“…[4], For a large size system we may neglect particle radiation from the surface and the baryon chemical potential is determined using the baryon number conservation…”

Transport theory beyond binary collisions

“…The problem of off-mass-shell transport has recently attracted a lot attention in the literature [31,32,33,34,35,36]. The collision term for off-mass-shell transport contains important contributions from one-and two-loop self-energy diagrams which correspond to 1 ↔ 2 and 1 ↔ 3 processes.…”

Thermodynamics of resonances and blurred particles

“…On the other hand, Refs. [5,6] have shown that, even with the full interaction included, the baryon density is presented as the sum of partial Noether contributions. Since we proved thermodynamic consistency of our "free resonance" model and recovered Noether quantities, we could hope that at least in the low density limit our ansatz (28), (41) and assumption, that terms ǫ int f − ǫ pot f being present in the pressure do not contribute to the particle density, are indeed .…”

“…Indeed, Refs. [5,6] have shown that expression for the total particle density, as the sum of the Noether densities (expressed entirely in terms of the A-spectral functions) fulfills thermodynamical consistency condition (first condition (3)). Namely using the latter condition Ref.…”