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Boltzmann equations are often used to describe the non-equilibriumtime-evolution of many-body systems in particle physics. Prominent examples arethe computation of the baryon asymmetry of the universe and the evolution ofthe quark-gluon plasma after a relativistic heavy ion collision. However,Boltzmann equations are only a classical approximation of the quantumthermalization process, which is described by so-called Kadanoff-Baymequations. This raises the question how reliable Boltzmann equations are asapproximations to the complete Kadanoff-Baym equations. Therefore, we presentin this article a detailed comparison of Boltzmann and Kadanoff-Baym equationsin the framework of a chirally invariant Yukawa-type quantum field theoryincluding fermions and scalars. The obtained numerical results revealsignificant differences between both types of equations. Apart fromquantitative differences, on a qualitative level the late-time universalityrespected by Kadanoff-Baym equations is severely restricted in the case ofBoltzmann equations. Furthermore, Kadanoff-Baym equations strongly separate thetime scales between kinetic and chemical equilibration. In contrast to thisstandard Boltzmann equations cannot describe the process of quantum-chemicalequilibration, and consequently also cannot feature the above separation oftime scales.

Comparison of Boltzmann Kinetics with Quantum Dynamics for a Chiral Yukawa Model Far From Equilibrium